{"id":29195,"date":"2018-07-18T06:07:18","date_gmt":"2018-07-18T06:07:18","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=29195"},"modified":"2020-12-02T11:46:33","modified_gmt":"2020-12-02T06:16:33","slug":"rs-aggarwal-solutions-class-10-chapter-3-linear-equations-in-two-variables","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/rs-aggarwal-solutions-class-10-chapter-3-linear-equations-in-two-variables\/","title":{"rendered":"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables"},"content":{"rendered":"<h2>RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables<\/h2>\n<p>These Solutions are part of <a href=\"https:\/\/cbselibrary.com\/rs-aggarwal-class-10-solutions\/\">RS Aggarwal Solutions Class 10<\/a>. Here we have given RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables<\/p>\n<h3 style=\"text-align: center;\"><strong><span style=\"color: #0000ff;\">Exercise 3A<\/span><\/strong><\/h3>\n<p><span style=\"color: #993366;\"><strong>Question 1:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118403\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-Q1.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Q1.1\" width=\"440\" height=\"43\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-Q1.1.png 440w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-Q1.1-300x29.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118012\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-1.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 1.1\" width=\"417\" height=\"323\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-1.1.png 417w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-1.1-300x232.png 300w\" sizes=\"(max-width: 417px) 100vw, 417px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118013\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-1.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 1.2\" width=\"442\" height=\"248\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-1.2.png 442w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-1.2-300x168.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118014\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-1.3.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 1.3\" width=\"493\" height=\"473\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-1.3.png 493w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-1.3-300x288.png 300w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/>h3<\/p>\n<p><strong>Read More:<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/cbselibrary.com\/what-is-a-linear-equation\/\"><span style=\"font-weight: 400;\">What is a Linear Equation<\/span><\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/linear-equations-in-one-variable\/\"><span style=\"font-weight: 400;\">Linear Equations In One Variable<\/span><\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/solution-of-linear-equation-two-variables\/\"><span style=\"font-weight: 400;\">Linear Equations In Two Variables<\/span><\/a><\/li>\n<li><a href=\"https:\/\/cbselibrary.com\/graphical-method\/\">Graphical Method Of Solving Linear Equations In Two Variables<\/a><\/li>\n<\/ul>\n<p><span style=\"color: #993366;\"><strong>Question 2:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118015\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-2.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 2.1\" width=\"456\" height=\"536\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-2.1.png 456w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-2.1-255x300.png 255w\" sizes=\"(max-width: 456px) 100vw, 456px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118016\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-2.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 2.2\" width=\"426\" height=\"398\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-2.2.png 426w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-2.2-300x280.png 300w\" sizes=\"(max-width: 426px) 100vw, 426px\" \/><\/p>\n<p><strong>More Resources<\/strong><\/p>\n<ul>\n<li><a title=\"RS Aggarwal Class 10 Solutions\" href=\"https:\/\/cbselibrary.com\/course\/rs-aggarwal-class-10-solutions\/\">RS Aggarwal Solutions Class 10<\/a><\/li>\n<li><a title=\"RD Sharma Class 10 Solutions\" href=\"http:\/\/www.learncbse.in\/rd-sharma-class-10-solutions\/\">RD Sharma Class 10 Solutions<\/a><\/li>\n<li><a title=\"NCERT Solutions Home Page\" href=\"http:\/\/www.learncbse.in\/ncert-solutions-2\/\">NCERT Solutions<\/a><\/li>\n<\/ul>\n<p><span style=\"color: #993366;\"><strong>Question 3:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118017\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3.1\" width=\"444\" height=\"469\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3.1.png 444w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3.1-284x300.png 284w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118018\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3.2\" width=\"393\" height=\"423\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3.2.png 393w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3.2-279x300.png 279w\" sizes=\"(max-width: 393px) 100vw, 393px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 4:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118205\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-4.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 4.1\" width=\"445\" height=\"501\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-4.1.png 445w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-4.1-266x300.png 266w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118206\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-4.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 4.2\" width=\"468\" height=\"440\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-4.2.png 468w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-4.2-300x282.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 5:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118207\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-5.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 5.1\" width=\"457\" height=\"531\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-5.1.png 457w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-5.1-258x300.png 258w\" sizes=\"(max-width: 457px) 100vw, 457px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118208\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-5.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 5.2\" width=\"406\" height=\"386\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-5.2.png 406w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-5.2-300x285.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 6:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118209\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-6.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 6.1\" width=\"492\" height=\"354\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-6.1.png 492w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-6.1-300x216.png 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118210\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-6.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 6.2\" width=\"491\" height=\"515\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-6.2.png 491w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-6.2-286x300.png 286w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 7:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118211\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-7.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 7.1\" width=\"499\" height=\"488\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-7.1.png 499w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-7.1-300x293.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118212\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-7.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 7.2\" width=\"492\" height=\"542\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-7.2.png 492w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-7.2-272x300.png 272w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 8:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118213\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-8.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 8.1\" width=\"497\" height=\"469\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-8.1.png 497w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-8.1-300x283.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118215\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-8.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 8.2\" width=\"488\" height=\"488\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-8.2.png 488w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-8.2-150x150.png 150w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-8.2-300x300.png 300w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-8.2-100x100.png 100w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 9:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118216\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-9.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 9.1\" width=\"485\" height=\"486\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-9.1.png 485w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-9.1-150x150.png 150w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-9.1-300x300.png 300w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-9.1-100x100.png 100w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118217\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-9.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 9.2\" width=\"496\" height=\"479\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-9.2.png 496w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-9.2-300x290.png 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 10:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118218\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-10.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 10.1\" width=\"493\" height=\"523\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-10.1.png 493w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-10.1-283x300.png 283w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118219\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-10.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 10.2\" width=\"490\" height=\"479\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-10.2.png 490w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-10.2-300x293.png 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 11:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118220\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-11.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 11.1\" width=\"498\" height=\"636\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-11.1.png 498w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-11.1-235x300.png 235w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118221\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-11.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 11.2\" width=\"501\" height=\"456\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-11.2.png 501w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-11.2-300x273.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 12:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118222\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-12.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 12.1\" width=\"486\" height=\"445\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-12.1.png 486w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-12.1-300x275.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118223\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-12.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 12.2\" width=\"477\" height=\"608\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-12.2.png 477w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-12.2-235x300.png 235w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 13:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118224\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-13.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 13.1\" width=\"481\" height=\"347\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-13.1.png 481w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-13.1-300x216.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118225\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-13.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 13.2\" width=\"481\" height=\"548\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-13.2.png 481w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-13.2-263x300.png 263w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 14:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118226\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-14.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 14.1\" width=\"493\" height=\"414\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-14.1.png 493w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-14.1-300x252.png 300w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118227\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-14.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 14.2\" width=\"501\" height=\"576\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-14.2.png 501w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-14.2-261x300.png 261w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 15:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118228\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-15.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 15.1\" width=\"499\" height=\"409\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-15.1.png 499w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-15.1-300x246.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118229\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-15.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 15.2\" width=\"499\" height=\"670\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-15.2.png 499w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-15.2-223x300.png 223w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 16:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118230\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-16.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 16.1\" width=\"494\" height=\"474\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-16.1.png 494w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-16.1-300x288.png 300w\" sizes=\"(max-width: 494px) 100vw, 494px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118231\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-16.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 16.2\" width=\"498\" height=\"602\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-16.2.png 498w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-16.2-248x300.png 248w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 17:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118232\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-17.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 17.1\" width=\"497\" height=\"421\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-17.1.png 497w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-17.1-300x254.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118233\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-17.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 17.2\" width=\"499\" height=\"517\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-17.2.png 499w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-17.2-290x300.png 290w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 18:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118234\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-18.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 18.1\" width=\"474\" height=\"536\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-18.1.png 474w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-18.1-265x300.png 265w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118235\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-18.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 18.2\" width=\"499\" height=\"495\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-18.2.png 499w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-18.2-150x150.png 150w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-18.2-300x298.png 300w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-18.2-100x100.png 100w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 19:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118236\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-19.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 19.1\" width=\"500\" height=\"510\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-19.1.png 500w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-19.1-294x300.png 294w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 20:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118237\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-20.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 20.1\" width=\"497\" height=\"368\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-20.1.png 497w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-20.1-300x222.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118238\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-20.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 20.2\" width=\"489\" height=\"587\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-20.2.png 489w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-20.2-250x300.png 250w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 21:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118240\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-21.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 21.1\" width=\"496\" height=\"486\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-21.1.png 496w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-21.1-300x294.png 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118241\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-21.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 21.2\" width=\"496\" height=\"665\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-21.2.png 496w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-21.2-224x300.png 224w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 22:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118242\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-22.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 22.1\" width=\"479\" height=\"464\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-22.1.png 479w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-22.1-300x291.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118243\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-22.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 22.2\" width=\"500\" height=\"642\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-22.2.png 500w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-22.2-234x300.png 234w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 23:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118244\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-23.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 23.1\" width=\"484\" height=\"484\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-23.1.png 484w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-23.1-150x150.png 150w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-23.1-300x300.png 300w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-23.1-100x100.png 100w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118245\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-23.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 23.2\" width=\"493\" height=\"590\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-23.2.png 493w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-23.2-251x300.png 251w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118246\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-23.3.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 23.3\" width=\"362\" height=\"128\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-23.3.png 362w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-23.3-300x106.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 24:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118247\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-24.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 24.1\" width=\"490\" height=\"471\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-24.1.png 490w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-24.1-300x288.png 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118248\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-24.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 24.2\" width=\"478\" height=\"390\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-24.2.png 478w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-24.2-300x245.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 25:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118249\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-25.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 25.1\" width=\"470\" height=\"313\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-25.1.png 470w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-25.1-300x200.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118250\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-25.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 25.2\" width=\"492\" height=\"501\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-25.2.png 492w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-25.2-295x300.png 295w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 26:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118251\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-26.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 26.1\" width=\"487\" height=\"495\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-26.1.png 487w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-26.1-295x300.png 295w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118252\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-26.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 26.2\" width=\"499\" height=\"330\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-26.2.png 499w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-26.2-300x198.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 27:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118253\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-27.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 27.1\" width=\"487\" height=\"171\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-27.1.png 487w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-27.1-300x105.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118254\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-27.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 27.2\" width=\"485\" height=\"292\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-27.2.png 485w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-27.2-300x181.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118255\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-27.3.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 27.3\" width=\"468\" height=\"444\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-27.3.png 468w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-27.3-300x285.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 28:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118256\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-28.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 28.1\" width=\"486\" height=\"443\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-28.1.png 486w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-28.1-300x273.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118257\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-28.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 28.2\" width=\"465\" height=\"396\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-28.2.png 465w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-28.2-300x255.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><\/p>\n<h3 style=\"text-align: center;\"><strong><span style=\"color: #0000ff;\">Exercise 3B<\/span><\/strong><\/h3>\n<p><span style=\"color: #993366;\"><strong>Question 1:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118019\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-1.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 1.1\" width=\"314\" height=\"251\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-1.1.png 314w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-1.1-300x240.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 2:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118020\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-2.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 2.1\" width=\"333\" height=\"209\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-2.1.png 333w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-2.1-300x188.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 3:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118021\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-3.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 3.1\" width=\"382\" height=\"230\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-3.1.png 382w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-3.1-300x181.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 4:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118022\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-4.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 4.1\" width=\"311\" height=\"228\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-4.1.png 311w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-4.1-300x220.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 5:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118024\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-5.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 5.1\" width=\"349\" height=\"262\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-5.1.png 349w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-5.1-300x225.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 6:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118025\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-6.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 6.1\" width=\"365\" height=\"281\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-6.1.png 365w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-6.1-300x231.png 300w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 7:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118026\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-7.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 7.1\" width=\"259\" height=\"377\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-7.1.png 259w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-7.1-206x300.png 206w\" sizes=\"(max-width: 259px) 100vw, 259px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 8:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118027\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-8.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 8.1\" width=\"256\" height=\"436\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-8.1.png 256w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-8.1-176x300.png 176w\" sizes=\"(max-width: 256px) 100vw, 256px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 9:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118028\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-9.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 9.1\" width=\"305\" height=\"272\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-9.1.png 305w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-9.1-300x268.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 10:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118029\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-10.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 10.1\" width=\"260\" height=\"247\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 11:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118030\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-11.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 11.1\" width=\"315\" height=\"209\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-11.1.png 315w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-11.1-300x199.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 12:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118031\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-12.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 12.1\" width=\"255\" height=\"450\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-12.1.png 255w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-12.1-170x300.png 170w\" sizes=\"(max-width: 255px) 100vw, 255px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 13:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118032\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-13.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 13.1\" width=\"275\" height=\"549\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-13.1.png 275w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-13.1-150x300.png 150w\" sizes=\"(max-width: 275px) 100vw, 275px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 14:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118033\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-14.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 14.1\" width=\"312\" height=\"477\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-14.1.png 312w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-14.1-196x300.png 196w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 15:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118034\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-15.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 15.1\" width=\"317\" height=\"442\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-15.1.png 317w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-15.1-215x300.png 215w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 16:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118035\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-16.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 16.1\" width=\"286\" height=\"573\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-16.1.png 286w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-16.1-150x300.png 150w\" sizes=\"(max-width: 286px) 100vw, 286px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 17:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118036\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-17.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 17.1\" width=\"388\" height=\"336\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-17.1.png 388w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-17.1-300x260.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 18:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118037\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-18.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 18.1\" width=\"340\" height=\"380\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-18.1.png 340w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-18.1-268x300.png 268w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 19:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118038\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-19.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 19.1\" width=\"254\" height=\"598\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-19.1.png 254w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-19.1-127x300.png 127w\" sizes=\"(max-width: 254px) 100vw, 254px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 20:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118039\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-20.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 20.1\" width=\"285\" height=\"552\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-20.1.png 285w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-20.1-155x300.png 155w\" sizes=\"(max-width: 285px) 100vw, 285px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 21:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118040\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-21.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 21.1\" width=\"311\" height=\"528\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-21.1.png 311w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-21.1-177x300.png 177w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 22:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118041\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-22.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 22.1\" width=\"127\" height=\"39\" \/><br \/>\nTaking L.C.M, we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118042\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-22.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 22.2\" width=\"228\" height=\"104\" \/><br \/>\nMultiplying (1) by 1 and (2) by<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118043\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-22.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 22.3\" width=\"215\" height=\"57\" \/><br \/>\nSubtracting (4) from (3), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118044\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-22.4.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 22.4\" width=\"204\" height=\"161\" \/><br \/>\nSubstituting x = ab in (3), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118045\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-22.5.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 22.5\" width=\"236\" height=\"127\" \/><br \/>\nTherefore solution is x = ab, y = ab<br \/>\n<span style=\"color: #993366;\"><strong>Question 23:<\/strong><\/span><br \/>\n6(ax + by) = 3a + 2b<br \/>\n6ax + 6by = 3a + 2b &#8212;(1)<br \/>\n6(bx &#8211; ay) = 3b &#8211; 2a<br \/>\n6bx &#8211; 6ay = 3b- 2a &#8212;(2)<br \/>\n6ax + 6by = 3a + 2b &#8212;(1)<br \/>\n6bx &#8211; 6ay = 3b &#8211; 2a &#8212;(2)<br \/>\nMultiplying (1) by a and (2) by b<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118046\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-23.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 23.1\" width=\"241\" height=\"57\" \/><br \/>\nAdding (3) and (4), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118047\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-23.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 23.2\" width=\"179\" height=\"125\" \/><br \/>\nSubstituting in (1), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118048\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-23.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 23.3\" width=\"187\" height=\"145\" \/><br \/>\nHence, the solution is<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118049\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-23.4.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 23.4\" width=\"74\" height=\"36\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 24:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118050\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-24.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 24.1\" width=\"280\" height=\"520\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-24.1.png 280w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-24.1-162x300.png 162w\" sizes=\"(max-width: 280px) 100vw, 280px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 25:<\/strong><\/span><br \/>\nThe given equations are<br \/>\n71x + 37y = 253 &#8212;(1)<br \/>\n37x + 71y = 287 &#8212;(2)<br \/>\nAdding (1) and (2)<br \/>\n108x + 108y = 540<br \/>\n108(x + y) = 540<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118051\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-25.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 25.1\" width=\"127\" height=\"39\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-25.1.gif 127w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-25.1-100x32.gif 100w\" sizes=\"(max-width: 127px) 100vw, 127px\" \/>&#8212;-(3)<br \/>\nSubtracting (2) from (1)<br \/>\n34x &#8211; 34y = 253 &#8211; 287 = -34<br \/>\n34(x &#8211; y) = -34<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118052\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-25.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 25.2\" width=\"141\" height=\"39\" \/>&#8212;(4)<br \/>\nAdding (3) and (4)<br \/>\n2x = 5 &#8211; 1= 4<br \/>\n\u21d2 x = 2<br \/>\nSubtracting (4) from (3)<br \/>\n2y = 5 + 1 = 6<br \/>\n\u21d2 y = 3<br \/>\nHence solution is x = 2, y = 3<br \/>\n<span style=\"color: #993366;\"><strong>Question 26:<\/strong><\/span><br \/>\n37x + 43y = 123 &#8212;-(1)<br \/>\n43x + 37y = 117 &#8212;-(2)<br \/>\nAdding (1) and (2)<br \/>\n80x + 80y = 240<br \/>\n80(x + y) = 240<br \/>\nx + y = <img loading=\"lazy\" class=\"alignnone size-full wp-image-118053\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-26.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 26.1\" width=\"49\" height=\"36\" \/>&#8212;-(3)<br \/>\nSubtracting (1) from (2),<br \/>\n6x &#8211; 6y = -6<br \/>\n6(x &#8211; y) = -6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118054\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3b-26.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3b 26.2\" width=\"118\" height=\"36\" \/>&#8212;-(4)<br \/>\nAdding (3) and (4)<br \/>\n2x = 3 &#8211; 1 = 2<br \/>\n\u21d2 x = 1<br \/>\nSubtracting (4) from (3),<br \/>\n2y = 3 + 1 = 4<br \/>\n\u21d2 y = 2<br \/>\nHence solution is x = 1, y = 2<br \/>\n<span style=\"color: #993366;\"><strong>Question 27:<\/strong><\/span><br \/>\n217x + 131y = 913 &#8212;(1)<br \/>\n131x + 217y = 827 &#8212;(2)<br \/>\nAdding (1) and (2), we get<br \/>\n348x + 348y = 1740<br \/>\n348(x + y) = 1740<br \/>\nx + y = 5 &#8212;-(3)<br \/>\nSubtracting (2) from (1), we get<br \/>\n86x &#8211; 86y = 86<br \/>\n86(x &#8211; y) = 86<br \/>\nx &#8211; y = 1 &#8212;(4)<br \/>\nAdding (3) and (4), we get<br \/>\n2x = 6<br \/>\nx = 3<br \/>\nputting x = 3 in (3), we get<br \/>\n3 + y = 5<br \/>\ny = 5 &#8211; 3 = 2<br \/>\nHence solution is x = 3, y = 2<br \/>\n<span style=\"color: #993366;\"><strong>Question 28:<\/strong><\/span><br \/>\n41x &#8211; 17y = 99 &#8212;(1)<br \/>\n17x &#8211; 41y = 75 &#8212;(2)<br \/>\nAdding (1) and (2), we get<br \/>\n58x &#8211; 58y = 174<br \/>\n58(x &#8211; y) = 174<br \/>\nx &#8211; y = 3 &#8212;(3)<br \/>\nsubtracting (2) from (1), we get<br \/>\n24x + 24y = 24<br \/>\n24(x + y) = 24<br \/>\nx + y = 1 &#8212;(4)<br \/>\nAdding (3) and (4), we get<br \/>\n2x = 4 x = 2<br \/>\nPutting x = 2 in (3), we get<br \/>\n2 &#8211; y = 3<br \/>\n-y = 3 &#8211; 2 y = -1<br \/>\nHence solution is x =2, y = -1<\/p>\n<h3 style=\"text-align: center;\"><strong><span style=\"color: #0000ff;\">Exercise 3C<\/span><\/strong><\/h3>\n<p><span style=\"color: #993366;\"><strong>Question 1:<\/strong><\/span><br \/>\nx + 2y + 1 = 0 &#8212;(1)<br \/>\n2x &#8211; 3y &#8211; 12 = 0 &#8212;(2)<br \/>\nBy cross multiplication, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118056\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-1.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 1.1\" width=\"433\" height=\"172\" \/><br \/>\nHence, x = 3 and y = -2 is the solution<br \/>\n<span style=\"color: #993366;\"><strong>Question 2:<\/strong><\/span><br \/>\n2x + 5y &#8211; 1 = 0 &#8212;(1)<br \/>\n2x + 3y &#8211; 3 = 0 &#8212;(2)<br \/>\nBy cross multiplication we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118057\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-2.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 2.1\" width=\"376\" height=\"204\" \/><br \/>\nHence the solution is x = 3, y = -1<br \/>\n<span style=\"color: #993366;\"><strong>Question 3:<\/strong><\/span><br \/>\n3x &#8211; 2y + 3 = 0<br \/>\n4x + 3y &#8211; 47 = 0<br \/>\nBy cross multiplication we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118058\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-3.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 3.1\" width=\"463\" height=\"233\" \/><br \/>\nHence the solution is x = 5, y = 9<br \/>\n<span style=\"color: #993366;\"><strong>Question 4:<\/strong><\/span><br \/>\n6x &#8211; 5y &#8211; 16 = 0<br \/>\n7x &#8211; 13y + 10 = 0<br \/>\nBy cross multiplication we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118060\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-4.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 4.1\" width=\"494\" height=\"203\" \/><br \/>\nHence the solution is x = 6, y = 4<br \/>\n<span style=\"color: #993366;\"><strong>Question 5:<\/strong><\/span><br \/>\n3x + 2y + 25 = 0<br \/>\n2x + y + 10 = 0<br \/>\nBy cross multiplication, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118061\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-5.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 5.1\" width=\"355\" height=\"165\" \/><br \/>\nHence the solution is x = 5, y = -20<br \/>\n<span style=\"color: #993366;\"><strong>Question 6:<\/strong><\/span><br \/>\n2x + y &#8211; 35 = 0<br \/>\n3x + 4y &#8211; 65 = 0<br \/>\nBy cross multiplication, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118062\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-6.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 6.1\" width=\"465\" height=\"236\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 7:<\/strong><\/span><br \/>\n7x &#8211; 2y &#8211; 3 = 0<br \/>\nBy cross multiplication, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118064\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-7.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 7.1\" width=\"352\" height=\"315\" \/><br \/>\nHence x = 1, y = 2 is the solution<br \/>\n<span style=\"color: #993366;\"><strong>Question 8:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118065\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-8.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 8.1\" width=\"381\" height=\"390\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-8.1.png 381w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-8.1-293x300.png 293w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 9:<\/strong><\/span><br \/>\nax + by &#8211; (a &#8211; b) = 0<br \/>\nbx &#8211; ay &#8211; (a + b) = 0<br \/>\nBy cross multiplication, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118066\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-9.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 9.1\" width=\"498\" height=\"328\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-9.1.png 498w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-9.1-300x198.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 10:<\/strong><\/span><br \/>\n2ax + 3by &#8211; (a + 2b) = 0<br \/>\n3ax + 2by &#8211; (2a + b) = 0<br \/>\nBy cross multiplication, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118067\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-10.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 10.1\" width=\"498\" height=\"375\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-10.1.png 498w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-10.1-300x226.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 11:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118068\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-11.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 11.1\" width=\"160\" height=\"73\" \/><br \/>\nBy cross multiplication, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118069\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-11.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 11.2\" width=\"474\" height=\"366\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-11.2.png 474w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-11.2-300x232.png 300w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 12:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118070\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-12.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 12.1\" width=\"160\" height=\"73\" \/><br \/>\nBy cross multiplication, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118071\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-12.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 12.2\" width=\"486\" height=\"405\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-12.2.png 486w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-12.2-300x250.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 13:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118072\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-13.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 13.1\" width=\"131\" height=\"83\" \/><br \/>\nBy cross multiplication we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118073\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-13.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 13.2\" width=\"505\" height=\"390\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-13.2.png 505w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-13.2-300x232.png 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 14:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118074\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-14.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 14.1\" width=\"104\" height=\"85\" \/><br \/>\nTaking<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118075\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-14.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 14.2\" width=\"123\" height=\"41\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-14.2.gif 123w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-14.2-100x34.gif 100w\" sizes=\"(max-width: 123px) 100vw, 123px\" \/><br \/>\nu + v &#8211; 7 = 0<br \/>\n2u + 3v &#8211; 17 = 0<br \/>\nBy cross multiplication, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118076\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-14.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 14.3\" width=\"377\" height=\"231\" \/><br \/>\nHence the solution is<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118077\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-14.4.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 14.4\" width=\"93\" height=\"39\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 15:<\/strong><\/span><br \/>\nLet<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118078\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-15.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 15.1\" width=\"172\" height=\"41\" \/><br \/>\nin the equation<br \/>\n5u &#8211; 2v + 1 = 0<br \/>\n15u + 7v &#8211; 10 = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118079\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-15.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 15.2\" width=\"481\" height=\"560\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-15.2.png 481w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-15.2-258x300.png 258w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 16:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118080\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-16.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3c 16.1\" width=\"442\" height=\"551\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-16.1.png 442w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3c-16.1-241x300.png 241w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<h3 style=\"text-align: center;\"><strong><span style=\"color: #0000ff;\">Exercise 3D<\/span><\/strong><\/h3>\n<p><span style=\"color: #993366;\"><strong>Question 1:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118081\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-1.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 1.1\" width=\"457\" height=\"433\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-1.1.png 457w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-1.1-300x284.png 300w\" sizes=\"(max-width: 457px) 100vw, 457px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 2:<\/strong><\/span><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118082\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-2.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 2.1\" width=\"444\" height=\"503\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-2.1.png 444w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-2.1-265x300.png 265w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 3:<\/strong><\/span><br \/>\n3x &#8211; 5y &#8211; 7 = 0<br \/>\n6x &#8211; 10y &#8211; 3 = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118083\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-3.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 3.1\" width=\"305\" height=\"135\" \/><br \/>\nHence the given system of equations is inconsistent<br \/>\n<span style=\"color: #993366;\"><strong>Question 4:<\/strong><\/span><br \/>\n2x &#8211; 3y &#8211; 5 = 0, 6x &#8211; 9y &#8211; 15 = 0<br \/>\nThese equations are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118084\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-4.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 4.1\" width=\"327\" height=\"159\" \/><br \/>\nHence the given system of equations has infinitely many solutions<br \/>\n<span style=\"color: #993366;\"><strong>Question 5:<\/strong><\/span><br \/>\nkx + 2y &#8211; 5 = 0<br \/>\n3x &#8211; 4y &#8211; 10 = 0<br \/>\nThese equations are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118085\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-5.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 5.1\" width=\"296\" height=\"136\" \/><br \/>\nThis happens when<br \/>\n\\(k\\neq \\frac { -3 }{ 2 }\\)<br \/>\nThus, for all real value of k other that , the given system equations will have a unique solution<br \/>\n(ii) For no solution we must have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118086\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-5.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 5.2\" width=\"99\" height=\"44\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118087\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-5.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 5.3\" width=\"161\" height=\"164\" \/><br \/>\nHence, the given system of equations has no solution if\u00a0\\(k=\\frac { -3 }{ 2 } \\)<br \/>\n<span style=\"color: #993366;\"><strong>Question 6:<\/strong><\/span><br \/>\nx + 2y &#8211; 5 = 0<br \/>\n3x + ky + 15 = 0<br \/>\nThese equations are of the form of<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118088\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-6.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 6.1\" width=\"296\" height=\"136\" \/><br \/>\nThus for all real value of k other than 6, the given system of equation will have unique solution<br \/>\n(ii) For no solution we must have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118089\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-6.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 6.2\" width=\"131\" height=\"124\" \/><br \/>\nTherefore k = 6<br \/>\nHence the given system will have no solution when k = 6.<br \/>\n<span style=\"color: #993366;\"><strong>Question 7:<\/strong><\/span><br \/>\nx + 2y &#8211; 3 = 0, 5x + ky + 7 = 0<br \/>\nThese equations are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118090\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-7.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 7.1\" width=\"404\" height=\"45\" \/><br \/>\n(i) For a unique solution we must have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118091\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-7.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 7.2\" width=\"135\" height=\"65\" \/><br \/>\nThus, for all real value of k other than 10<br \/>\nThe given system of equation will have a unique solution.<br \/>\n(ii) For no solution we must have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118092\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-7.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 7.3\" width=\"229\" height=\"124\" \/><br \/>\nHence the given system of equations has no solution if<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118093\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-7.4.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 7.4\" width=\"116\" height=\"39\" \/><br \/>\nFor infinite number of solutions we must have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118094\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-7.5.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 7.5\" width=\"97\" height=\"84\" \/><br \/>\nThis is never possible since<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118095\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-7.6.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 7.6\" width=\"53\" height=\"39\" \/><br \/>\nThere is no value of k for which system of equations has infinitely many solutions<br \/>\n<span style=\"color: #993366;\"><strong>Question 8:<\/strong><\/span><br \/>\n8x + 5y &#8211; 9 = 0<br \/>\nkx + 10y &#8211; 15 = 0<br \/>\nThese equations are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118096\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-8.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 8.1\" width=\"333\" height=\"317\" \/><br \/>\nClearly, k = 16 also satisfies the condition<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118097\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-8.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 8.2\" width=\"52\" height=\"39\" \/><br \/>\nHence, the given system will have no solution when k = 16.<br \/>\n<span style=\"color: #993366;\"><strong>Question 9:<\/strong><\/span><br \/>\nkx + 3y &#8211; 3 = 0 &#8212;-(1)<br \/>\n12x + ky &#8211; 6 = 0 &#8212;(2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118098\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-9.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 9.1\" width=\"172\" height=\"45\" \/><br \/>\nThese equations are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118099\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-9.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 9.2\" width=\"324\" height=\"240\" \/><br \/>\nHence, the given system will have no solution when k = -6<br \/>\n<span style=\"color: #993366;\"><strong>Question 10:<\/strong><\/span><br \/>\n3x + y &#8211; 1 = 0<br \/>\n(2k &#8211; 1)x + (k &#8211; 1)y &#8211; (2k + 1) = 0<br \/>\nThese equations are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118100\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-10.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 10.1\" width=\"351\" height=\"293\" \/><br \/>\nThus,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118101\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-10.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 10.2\" width=\"223\" height=\"44\" \/><br \/>\nHence the given equation has no solution when k = 2<br \/>\n<span style=\"color: #993366;\"><strong>Question 11:<\/strong><\/span><br \/>\n(3k + 1)x + 3y &#8211; 2 = 0<br \/>\n(k<sup>2<\/sup> + 1)x + (k &#8211; 2)y &#8211; 5 = 0<br \/>\nthese equations are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118102\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-11.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 11.1\" width=\"336\" height=\"360\" \/><br \/>\nThus, k = -1 also satisfy the condition<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118103\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-11.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 11.2\" width=\"51\" height=\"39\" \/><br \/>\nHence, the given system will have no solution when k = -1<br \/>\n<span style=\"color: #993366;\"><strong>Question 12:<\/strong><\/span><br \/>\nThe given equations are<br \/>\n3x &#8211; y &#8211; 5 = 0 &#8212;(1)<br \/>\n6x &#8211; 2y + k = 0&#8212;(2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118104\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-12.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 12.1\" width=\"263\" height=\"91\" \/><br \/>\nEquations (1) and (2) have no solution, if<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118105\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-12.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 12.2\" width=\"141\" height=\"39\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 13:<\/strong><\/span><br \/>\nkx + 2y &#8211; 5 = 0<br \/>\n3x + y &#8211; 1 = 0<br \/>\nThese equations are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118106\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-13.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 13.1\" width=\"319\" height=\"180\" \/><br \/>\nThus, for all real values of k other than 6, the given system of equations will have a unique solution<br \/>\n<span style=\"color: #993366;\"><strong>Question 14:<\/strong><\/span><br \/>\nx &#8211; 2y &#8211; 3 = 0<br \/>\n3x + ky &#8211; 1 = 0<br \/>\nThese equations are of the form of<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118107\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-14.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 14.1\" width=\"283\" height=\"176\" \/><br \/>\nThus, for all real value of k other than -6, the given system of equations will have a unique solution<br \/>\n<span style=\"color: #993366;\"><strong>Question 15:<\/strong><\/span><br \/>\nkx + 3y &#8211; (k &#8211; 3) = 0<br \/>\n12x + ky &#8211; k = 0<br \/>\nThese equations are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118108\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-15.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 15.1\" width=\"304\" height=\"204\" \/><br \/>\nThus, for all real value of k other than , the given system of equations will have a unique solution<br \/>\n<span style=\"color: #993366;\"><strong>Question 16:<\/strong><\/span><br \/>\n4x &#8211; 5y &#8211; k = 0, 2x &#8211; 3y &#8211; 12 = 0<br \/>\nThese equations are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118109\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-16.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 16.1\" width=\"296\" height=\"216\" \/><br \/>\nThus, for all real value of k the given system of equations will have a unique solution<br \/>\n<span style=\"color: #993366;\"><strong>Question 17:<\/strong><\/span><br \/>\n2x + 3y &#8211; 7 = 0<br \/>\n(k &#8211; 1)x + (k + 2)y &#8211; 3k = 0<br \/>\nThese are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118110\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-17.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 17.1\" width=\"331\" height=\"137\" \/><br \/>\nThis hold only when<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118111\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-17.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 17.2\" width=\"139\" height=\"79\" \/><br \/>\nNow the following cases arises<br \/>\nCase : I<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118112\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-17.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 17.3\" width=\"278\" height=\"87\" \/><br \/>\nCase: II<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118113\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-17.4.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 17.4\" width=\"237\" height=\"86\" \/><br \/>\nCase III<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118114\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-17.5.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 17.5\" width=\"101\" height=\"80\" \/><br \/>\nFor k = 7, there are infinitely many solutions of the given system of equations<br \/>\n<span style=\"color: #993366;\"><strong>Question 18:<\/strong><\/span><br \/>\n2x + (k &#8211; 2)y &#8211; k = 0<br \/>\n6x + (2k &#8211; 1)y &#8211; (2k + 5) = 0<br \/>\nThese are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118115\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-18.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 18.1\" width=\"304\" height=\"73\" \/><br \/>\nFor infinite number of solutions, we have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118116\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-18.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 18.2\" width=\"97\" height=\"44\" \/><br \/>\nThis hold only when<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118118\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-18.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 18.3\" width=\"161\" height=\"84\" \/><br \/>\nCase (1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118119\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-18.4.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 18.4\" width=\"211\" height=\"59\" \/><br \/>\nCase (2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118120\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-18.5.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 18.5\" width=\"291\" height=\"153\" \/><br \/>\nCase (3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118121\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-18.6.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 18.6\" width=\"181\" height=\"83\" \/><br \/>\nThus, for k = 5 there are infinitely many solutions<br \/>\n<span style=\"color: #993366;\"><strong>Question 19:<\/strong><\/span><br \/>\nkx + 3y &#8211; (2k +1) = 0<br \/>\n2(k + 1)x + 9y &#8211; (7k + 1) = 0<br \/>\nThese are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118123\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-19.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 19.1\" width=\"309\" height=\"73\" \/><br \/>\nFor infinitely many solutions, we must have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118124\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-19.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 19.2\" width=\"97\" height=\"44\" \/><br \/>\nThis hold only when<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118125\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-19.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 19.3\" width=\"195\" height=\"92\" \/><br \/>\nNow, the following cases arise<br \/>\nCase &#8211; (1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118126\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-19.4.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 19.4\" width=\"239\" height=\"92\" \/><br \/>\nCase (2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118127\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-19.5.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 19.5\" width=\"231\" height=\"83\" \/><br \/>\nCase (3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118128\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-19.6.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 19.6\" width=\"269\" height=\"165\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118129\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-19.7.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 19.7\" width=\"193\" height=\"172\" \/><br \/>\nThus, k = 2, is the common value for which there are infinitely many solutions<br \/>\n<span style=\"color: #993366;\"><strong>Question 20:<\/strong><\/span><br \/>\n5x + 2y &#8211; 2k = 0<br \/>\n2(k +1)x + ky &#8211; (3k + 4) = 0<br \/>\nThese are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118130\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-20.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 20.1\" width=\"315\" height=\"72\" \/><br \/>\nFor infinitely many solutions, we must have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118131\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-20.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 20.2\" width=\"97\" height=\"44\" \/><br \/>\nThese hold only when<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118132\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-20.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 20.3\" width=\"200\" height=\"89\" \/><br \/>\nCase I<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118133\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-20.4.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 20.4\" width=\"289\" height=\"92\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118134\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-20.5.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 20.5\" width=\"269\" height=\"307\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118135\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-20.6.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 20.6\" width=\"316\" height=\"237\" \/><br \/>\nThus, k = 4 is a common value for which there are infinitely by many solutions.<br \/>\n<span style=\"color: #993366;\"><strong>Question 21:<\/strong><\/span><br \/>\nx + (k + 1)y &#8211; 5 = 0<br \/>\n(k + 1)x + 9y &#8211; (8k &#8211; 1) = 0<br \/>\nThese are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118136\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-21.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 21.1\" width=\"328\" height=\"73\" \/><br \/>\nFor infinitely many solutions, we must have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118137\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-21.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 21.2\" width=\"381\" height=\"653\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-21.2.png 381w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-21.2-175x300.png 175w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 22:<\/strong><\/span><br \/>\n(k &#8211; 1)x &#8211; y &#8211; 5 = 0<br \/>\n(k + 1)x + (1 &#8211; k)y &#8211; (3k + 1) = 0<br \/>\nThese are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118138\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-22.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 22.1\" width=\"324\" height=\"73\" \/><br \/>\nFor infinitely many solution, we must now<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118139\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-22.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 22.2\" width=\"328\" height=\"744\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-22.2.png 328w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-22.2-132x300.png 132w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nk = 3 is common value for which the number of solutions is infinitely many<br \/>\n<span style=\"color: #993366;\"><strong>Question 23:<\/strong><\/span><br \/>\n(a &#8211; 1)x + 3y &#8211; 2 = 0<br \/>\n6x + (1 &#8211; 2b)y &#8211; 6 = 0<br \/>\nThese equations are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118140\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-23.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 23.1\" width=\"324\" height=\"73\" \/><br \/>\nFor infinite many solutions, we must have<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118141\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-23.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 23.2\" width=\"225\" height=\"351\" \/><br \/>\nHence a = 3 and b = -4<br \/>\n<span style=\"color: #993366;\"><strong>Question 24:<\/strong><\/span><br \/>\n(2a &#8211; 1)x + 3y &#8211; 5 = 0<br \/>\n3x + (b &#8211; 1)y &#8211; 2 = 0<br \/>\nThese equations are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118142\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-24.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 24.1\" width=\"296\" height=\"73\" \/><br \/>\nThese holds only when<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118143\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-24.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 24.2\" width=\"200\" height=\"355\" \/><br \/>\n<span style=\"color: #993366;\"><strong>Question 25:<\/strong><\/span><br \/>\n2x &#8211; 3y &#8211; 7 = 0<br \/>\n(a + b)x + (a + b &#8211; 3)y &#8211; (4a + b) = 0<br \/>\nThese equation are of the form<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118144\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-25.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 25.1\" width=\"365\" height=\"72\" \/><br \/>\nFor infinite number of solution<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118145\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-25.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 25.2\" width=\"323\" height=\"252\" \/><br \/>\nPutting a = 5b in (2), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118146\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-25.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 25.3\" width=\"136\" height=\"104\" \/><br \/>\nPutting b = -1 in (1), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118147\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-25.4.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 25.4\" width=\"95\" height=\"64\" \/><br \/>\nThus, a = -5, b = -1<br \/>\n<span style=\"color: #993366;\"><strong>Question 27:<\/strong><\/span><br \/>\nThe given equations are<br \/>\n2x + 3y = 7 &#8212;-(1)<br \/>\na(x + y) &#8211; b(x &#8211; y) = 3a + b &#8211; 2 &#8212;(2)<br \/>\nEquation (2) is<br \/>\nax + ay &#8211; bx + by = 3a + b &#8211; 2<br \/>\n(a &#8211; b)x + (a + b)y = 3a + b -2<br \/>\nComparing with the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118148\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-27.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 27.1\" width=\"303\" height=\"72\" \/><br \/>\nThere are infinitely many solution<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118149\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-27.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 27.2\" width=\"269\" height=\"124\" \/><br \/>\n2a + 2b = 3a &#8211; 3b and 3(3a + b &#8211; 2) = 7(a + b)<br \/>\n-a = -5b and 9a + 3b &#8211; 6 = 7a + 7b<br \/>\na = 5b and 9a &#8211; 7a + 3b &#8211; 7b = 6<br \/>\nor 2a &#8211; 4b = 6<br \/>\nor a &#8211; 2b = 3<br \/>\nthus equation in a, b are<br \/>\na = 5b &#8212;(3)<br \/>\na &#8211; 2b = 3 &#8212;(4)<br \/>\nputting a = 5b in (4)<br \/>\n5b &#8211; 2b = 3 or 3b = 3 \u00de b = 1<br \/>\nPutting b = 1 in (3)<br \/>\na = 5 and b = 1<br \/>\n<span style=\"color: #993366;\"><strong>Question 28:<\/strong><\/span><br \/>\nWe have 5x &#8211; 3y = 0 &#8212;(1)<br \/>\n2x + ky = 0 &#8212;(2)<br \/>\nComparing the equation with<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118150\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-28.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 28.1\" width=\"268\" height=\"45\" \/><br \/>\nThese equations have a non &#8211; zero solution if<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118151\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-28.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 28.2\" width=\"61\" height=\"44\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118152\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3d-28.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3d 28.3\" width=\"131\" height=\"79\" \/><\/p>\n<h3 style=\"text-align: center;\"><strong><span style=\"color: #0000ff;\">Exercise 3E<\/span><\/strong><\/h3>\n<p><span style=\"color: #993366;\"><strong>Question 1:<\/strong><\/span><br \/>\nLet the cost of 1 chair be Rs x and the cost of one table be Rs. y<br \/>\nThe cost of 5 chairs and 4 tables = Rs(5x + 4y) = Rs. 2800<br \/>\n5x + 4y = 2800 &#8212;(1)<br \/>\nThe cost of 4 chairs and 3 tables = Rs(4x + 3y) = Rs. 2170<br \/>\n4x + 3y = 2170 &#8212;(2)<br \/>\nMultiplying (1) by 3 and (2) by 4, we get<br \/>\n15x + 12y = 8400 &#8212;(3)<br \/>\n16x + 12y = 8680 &#8212;(4)<br \/>\nSubtracting (3) and (4), we get<br \/>\nx = 280<br \/>\nPutting value of x in (1), we get<br \/>\n5 \u00d7 280 + 4y = 2800<br \/>\nor 1400 + 4y = 2800<br \/>\nor 4y = 1400<br \/>\n\\(y=\\frac { 1400 }{ 4 } =350 \\)<br \/>\nThus, cost of 1 chair = Rs. 280 and cost of 1 table = Rs. 350<br \/>\n<span style=\"color: #993366;\"><strong>Question 2:<\/strong><\/span><br \/>\nLet the cost of a pen and a pencil be Rs x and Rs y respectively<br \/>\nCost of 37 pens and 53 pencils = Rs(37x + 53y) = Rs 820<br \/>\n37x + 53y = 820 &#8212;(1)<br \/>\nCost of 53 pens and 37 pencils = Rs(53x + 37y) = Rs 980<br \/>\n53x + 37y = 980 &#8212;(2)<br \/>\nAdding (1) and (2), we get<br \/>\n90x + 90y = 1800<br \/>\nx + y = 20 &#8212;(3)<br \/>\ny = 20 &#8211; x<br \/>\nPutting value of y in (1), we get<br \/>\n37x + 53(20 &#8211; x) = 820<br \/>\n37x + 1060 &#8211; 53x = 820<br \/>\n16x = 240<br \/>\n\\(x=\\frac { 240 }{ 16} =15 \\)<br \/>\nFrom (3), y = 20 &#8211; x = 20 &#8211; 15 = 5<br \/>\nx = 15, y = 5<br \/>\nThus, cost of a pen = Rs 15 and cost of pencil = Rs 5<br \/>\n<span style=\"color: #993366;\"><strong>Question 3:<\/strong><\/span><br \/>\nLet the number of 20 P and 25 P coins be x and y respectively<br \/>\nTotal number of coins x + y = 50<br \/>\ni.e., x + y = 50 &#8212;(1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118153\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-3.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 3.1\" width=\"409\" height=\"107\" \/><br \/>\nMultiplying (1) by 5 and (2) by 1, we get<br \/>\n5x + 5y = 250 &#8212;(3)<br \/>\n4x + 5y = 230 &#8212;(4)<br \/>\nSubtracting (4) from (3), we get<br \/>\nx = 20<br \/>\nPutting x = 20 in (1),<br \/>\ny = 50 &#8211; x<br \/>\n= 50 &#8211; 20<br \/>\n= 30<br \/>\nHence, number of 20 P coins = 20 and number of 25 P coins = 30<br \/>\n<span style=\"color: #993366;\"><strong>Question 4:<\/strong><\/span><br \/>\nLet the two numbers be x and y respectively.<br \/>\nGiven:<br \/>\nx + y = 137 &#8212;(1)<br \/>\nx &#8211; y = 43 &#8212;(2)<br \/>\nAdding (1) and (2), we get<br \/>\n2x = 180<br \/>\n\\(y=\\frac { 180\u00a0}{\u00a02} =90 \\)<br \/>\nPutting x = 90 in (1), we get<br \/>\n90 + y = 137<br \/>\ny = 137 &#8211; 90<br \/>\n= 47<br \/>\nHence, the two numbers are 90 and 47.<br \/>\n<span style=\"color: #993366;\"><strong>Question 5:<\/strong><\/span><br \/>\nLet the first and second number be x and y respectively.<br \/>\nAccording to the question:<br \/>\n2x + 3y = 92 &#8212;(1)<br \/>\n4x &#8211; 7y = 2 &#8212;(2)<br \/>\nMultiplying (1) by 7 and (2) by 3, we get<br \/>\n14 x+ 21y = 644 &#8212;(3)<br \/>\n12x &#8211; 21y = 6 &#8212;(4)<br \/>\nAdding (3) and (4), we get<br \/>\n\\(26x=650\\\\ x=\\frac { 650\u00a0}{ 26 } =25 \\)[\/latex]<br \/>\nPutting x = 25 in (1), we get<br \/>\n2 \u00d7 25 + 3y = 92<br \/>\n50 + 3y = 92<br \/>\n3y = 92 &#8211; 50<br \/>\n\\(y=\\frac { 42\u00a0}{ 3\u00a0} =14 \\)<br \/>\ny = 14<br \/>\n<span style=\"color: #993366;\"><strong>Question 6:<\/strong><\/span><br \/>\nLet the first and second numbers be x and y respectively.<br \/>\nAccording to the question:<br \/>\n3x + y = 142 &#8212;(1)<br \/>\n4x &#8211; y = 138 &#8212;(2)<br \/>\nAdding (1) and (2), we get<br \/>\n\\(7x=280\\\\x=\\frac { 280\u00a0}{ 7\u00a0} =40\u00a0\\)<br \/>\nPutting x = 40 in (1), we get<br \/>\n3 \u00d7 40 + y = 142<br \/>\ny = 142 &#8211; 120<br \/>\ny = 22<br \/>\nHence, the first and second numbers are 40 and 22.<br \/>\n<span style=\"color: #993366;\"><strong>Question 7:<\/strong><\/span><br \/>\nLet the greater number be x and smaller be y respectively.<br \/>\nAccording to the question:<br \/>\n2x &#8211; 45 = y<br \/>\n2x &#8211; y = 45 &#8212;(1)<br \/>\nand<br \/>\n2y &#8211; x = 21<br \/>\n-x + 2y = 21 &#8212;(2)<br \/>\nMultiplying (1) by 2 and (2) by 1<br \/>\n4x &#8211; 2y = 90 &#8212;(3)<br \/>\n-x + 2y = 21 &#8212;(4)<br \/>\nAdding (3) and (4), we get<br \/>\n3x = 111<br \/>\n\\(x=\\frac { 111\u00a0}{ 3\u00a0} =37 \\)<br \/>\nPutting x = 37 in (1), we get<br \/>\n2 \u00d7 37 &#8211; y = 45<br \/>\n74 &#8211; y = 45<br \/>\ny = 29<br \/>\nHence, the greater and the smaller numbers are 37 and 29.<br \/>\n<span style=\"color: #993366;\"><strong>Question 8:<\/strong><\/span><br \/>\nLet the larger number be x and smaller be y respectively.<br \/>\nWe know,<br \/>\nDividend = Divisor \u00d7 Quotient + Remainder<br \/>\n3x = y \u00d7 4 + 8<br \/>\n3x &#8211; 4y = 8 &#8212;(1)<br \/>\nAnd<br \/>\n5y = x \u00d7 3 + 5<br \/>\n-3x + 5y = 5 &#8212;(2)<br \/>\nAdding (1) and (2), we get<br \/>\ny = 13<br \/>\nputting y = 13 in (1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118154\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-8.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 8.1\" width=\"409\" height=\"107\" \/><br \/>\nHence, the larger and smaller numbers are 20 and 13 respectively.<br \/>\n<span style=\"color: #993366;\"><strong>Question 9:<\/strong><\/span><br \/>\nLet the required numbers be x and y respectively.<br \/>\nThen,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118155\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-9.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 9.1\" width=\"351\" height=\"85\" \/><br \/>\nTherefore,<br \/>\n2x &#8211; y = -2 &#8212;(1)<br \/>\n11x &#8211; 5y = 24 &#8212;(2)<br \/>\nMultiplying (1) by 5 and (2) by 1<br \/>\n10x &#8211; 5y = -10 &#8212;(3)<br \/>\n11x &#8211; 5y = 24 &#8212;(4)<br \/>\nSubtracting (3) and (4) we get<br \/>\nx = 34<br \/>\nputting x = 34 in (1), we get<br \/>\n2 \u00d7 34 &#8211; y = -2<br \/>\n68 &#8211; y = -2<br \/>\n-y = -2 &#8211; 68<br \/>\ny = 70<br \/>\nHence, the required numbers are 34 and 70.<br \/>\n<span style=\"color: #993366;\"><strong>Question 10:<\/strong><\/span><br \/>\nLet the numbers be x and y respectively.<br \/>\nAccording to the question:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118156\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-10.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 10.1\" width=\"165\" height=\"29\" \/><br \/>\nx &#8211; y = 14 &#8212;(1)<br \/>\nFrom (1), we get<br \/>\nx = 14 + y &#8212;(3)<br \/>\nputting x = 14 + y in (2), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118157\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-10.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 10.2\" width=\"189\" height=\"140\" \/><br \/>\nPutting y = 9 in (1), we get<br \/>\nx &#8211; 9 = 14<br \/>\nx = 14 + 9 = 23<br \/>\nHence the required numbers are 23 and 9<br \/>\n<span style=\"color: #993366;\"><strong>Question 11:<\/strong><\/span><br \/>\nLet the ten&#8217;s digit be x and units digit be y respectively.<br \/>\nThen,<br \/>\nx + y = 12 &#8212;(1)<br \/>\nLet the ten&#8217;s digit of required number be x and its unit&#8217;s digit be y respectively<br \/>\nRequired number = 10x + y<br \/>\n10x + y = 7(x + y)<br \/>\n10x + y = 7x + 7y<br \/>\n3x &#8211; 6y = 0 &#8212;(1)<br \/>\nNumber found on reversing the digits = 10y + x<br \/>\n(10x + y) &#8211; 27 = 10y + x<br \/>\n10x &#8211; x + y &#8211; 10y = 27<br \/>\n9x &#8211; 9y = 27<br \/>\n(x &#8211; y) = 27<br \/>\nx &#8211; y = 3 &#8212;(2)<br \/>\nMultiplying (1) by 1 and (2) by 6<br \/>\n3x &#8211; 6y = 0 &#8212;(3)<br \/>\n6x &#8211; 6y = 18 &#8212;(4)<br \/>\nSubtracting (3) from (4), we get<br \/>\n\\(3x=18\\\\ x=\\frac { 18 }{ 3\u00a0} =6 \\)<br \/>\nPutting x = 6 in (1), we get<br \/>\n3 \u00d7 6 &#8211; 6y = 0<br \/>\n18 &#8211; 6y = 0<br \/>\n\\(-6y=-18\\\\ y=\\frac { -18 }{ -6 } =3 \\)<br \/>\nNumber = 10x + y<br \/>\n= 10 \u00d7 6 + 3<br \/>\n= 60 + 3<br \/>\n= 63<br \/>\nHence the number is 63.<br \/>\n<span style=\"color: #993366;\"><strong>Question 12:<\/strong><\/span><br \/>\nLet the ten&#8217;s digit and unit&#8217;s digits of required number be x and y respectively.<br \/>\nRequired number = 10x + y<br \/>\nNumber obtained on reversing digits = 10y + x<br \/>\nAccording to the question:<br \/>\n10y + x \u00d7 (10x + y) = 18<br \/>\n10y + x &#8211; 10x &#8211; y = 18<br \/>\n9y &#8211; 9x = 18<br \/>\ny &#8211; x = 2 &#8212;-(2)<br \/>\nAdding (1) and (2), we get<br \/>\n\\(2y=14\\\\ y=\\frac { 14 }{ 2 } =7 \\)<br \/>\nPutting y = 7 in (1), we get<br \/>\nx + 7 = 12<br \/>\nx = 5<br \/>\nNumber = 10x + y<br \/>\n= 10 \u00d7 5 + 7<br \/>\n= 50 + 7<br \/>\n= 57<br \/>\nHence, the number is 57.<br \/>\n<span style=\"color: #993366;\"><strong>Question 13:<\/strong><\/span><br \/>\nLet the ten&#8217;s digit and unit&#8217;s digits of required number be x and y respectively.<br \/>\nThen,<br \/>\nx + y = 15 &#8212;(1)<br \/>\nRequired number = 10x + y<br \/>\nNumber obtained by interchanging the digits = 10y + x<br \/>\n10y + x \u00d7 (10x + y) = 9<br \/>\n10y + x &#8211; 10x &#8211; y = 9<br \/>\n9y &#8211; 9x = 9<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118409\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-Q13.1.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Q13.1\" width=\"116\" height=\"86\" \/><br \/>\nAdd (1) and (2), we get<br \/>\n\\(2y=16\\\\ y=\\frac { 16 }{ 2 } =8 \\)<br \/>\nPutting y = 8 in (1), we get<br \/>\nx + 8 = 15<br \/>\nx = 15 &#8211; 8 = 7<br \/>\nRequired number = 10x + y<br \/>\n= 10 \u00d7 7 + 8<br \/>\n= 70 + 8<br \/>\n= 78<br \/>\nHence the required number is 78.<br \/>\n<span style=\"color: #993366;\"><strong>Question 14:<\/strong><\/span><br \/>\nLet the ten&#8217;s and unit&#8217;s of required number be x and y respectively.<br \/>\nThen, required number =10x + y<br \/>\nAccording to the given question:<br \/>\n10x + y = 4(x + y) + 3<br \/>\n10x + y = 4x + 4y + 3<br \/>\n6x &#8211; 3y = 3<br \/>\n2x &#8211; y = 1 &#8212;(1)<br \/>\nAnd<br \/>\n10x + y + 18 = 10y + x<br \/>\n9x &#8211; 9y = -18<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118412\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-Q14.1.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Q14.1\" width=\"91\" height=\"49\" \/><br \/>\nx &#8211; y = -2 &#8212;(2)<br \/>\nSubtracting (2) from (1), we get<br \/>\nx = 3<br \/>\nPutting x = 3 in (1), we get<br \/>\n2 \u00d7 3 &#8211; y = 1<br \/>\ny = 6 &#8211; 1 = 5<br \/>\nx = 3, y = 5<br \/>\nRequired number = 10x + y<br \/>\n= 10 \u00d7 3 + 5<br \/>\n= 30 + 5<br \/>\n= 35<br \/>\nHence, required number is 35.<br \/>\n<span style=\"color: #993366;\"><strong>Question 15:<\/strong><\/span><br \/>\nLet the ten&#8217;s digit and unit&#8217;s digit of required number be x and y respectively.<br \/>\nWe know,<br \/>\nDividend = (divisor \u00d7 quotient) + remainder<br \/>\nAccording to the given questiion:<br \/>\n10x + y = 6 \u00d7 (x + y) + 0<br \/>\n10x &#8211; 6x + y &#8211; 6y = 0<br \/>\n4x &#8211; 5y = 0 &#8212;(1)<br \/>\nNumber obtained by reversing the digits is 10y + x<br \/>\n10x + y &#8211; 9 = 10y + x<br \/>\n9x &#8211; 9y = 9<br \/>\n9(x &#8211; y) = 9<br \/>\n(x &#8211; y) = 1 &#8212;(2)<br \/>\nMultiplying (1) by 1 and (2) by 5, we get<br \/>\n4x &#8211; 5y = 0 &#8212;(3)<br \/>\n5x &#8211; 5y = 5 &#8212;(4)<br \/>\nSubtracting (3) from (4), we get<br \/>\nx = 5<br \/>\nPutting x = 5 in (1), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118413\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-Q15.1.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Q15.1\" width=\"85\" height=\"62\" \/><br \/>\nx =5 and y = 4<br \/>\nHence, required number is 54.<br \/>\n<span style=\"color: #993366;\"><strong>Question 16:<\/strong><\/span><br \/>\nLet the ten&#8217;s and unit&#8217;s digits of the required number be x and y respectively.<br \/>\nThen, xy = 35<br \/>\nRequired number = 10x + y<br \/>\nAlso,<br \/>\n(10x + y) + 18 = 10y + x<br \/>\n9x &#8211; 9y = -18<br \/>\n9(y &#8211; x) = 18 &#8212;(1)<br \/>\ny &#8211; x = 2<br \/>\nNow,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118158\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-16.1.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 16.1\" width=\"169\" height=\"155\" \/><br \/>\nAdding (1) and (2),<br \/>\n2y = 12 + 2 = 14<br \/>\ny = 7<br \/>\nPutting y = 7 in (1),<br \/>\n7 &#8211; x = 2<br \/>\nx = 5<br \/>\nHence, the required number = 5 \u00d7 10 + 7<br \/>\n= 57<br \/>\n<span style=\"color: #993366;\"><strong>Question 17:<\/strong><\/span><br \/>\nLet the ten&#8217;s and units digit of the required number be x and y respectively.<br \/>\nThen, xy = 14<br \/>\nRequired number = 10x + y<br \/>\nNumber obtained on reversing the digits = 10y + x<br \/>\nAlso,<br \/>\n(10x + y) + 45 = 10y + x<br \/>\n9(y &#8211; x) = 45<br \/>\ny &#8211; x = 5 &#8212;(1)<br \/>\nNow,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118159\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-17.1.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 17.1\" width=\"136\" height=\"23\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118160\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-17.2.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 17.2\" width=\"154\" height=\"64\" \/><br \/>\ny + x = 9 &#8212;(2) (digits cannot be negative, hence -9 is not possible)<br \/>\nOn adding (1) and (2), we get<br \/>\n2y = 14<br \/>\ny = 7<br \/>\nPutting y = 7 in (2), we get<br \/>\n7 + x = 9<br \/>\nx = (9 &#8211; 7) = 2<br \/>\nx = 2 and y = 7<br \/>\nHence, the required number is = 2 \u00d7\u00a010 + 7<br \/>\n= 27<br \/>\n<span style=\"color: #993366;\"><strong>Question 18:<\/strong><\/span><br \/>\nLet the ten&#8217;s and unit&#8217;s digits of the required number be x and y respectively.<br \/>\nThen, xy = 18<br \/>\nRequired number = 10x + y<br \/>\nNumber obtained on reversing its digits = 10y + x<br \/>\n(10x + y) &#8211; 63 = (10y + x)<br \/>\n9x &#8211; 9y = 63<br \/>\nx &#8211; y = 7 &#8212;(1)<br \/>\nNow,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118161\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-18.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 18.1\" width=\"175\" height=\"31\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118162\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-18.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 18.2\" width=\"320\" height=\"93\" \/><br \/>\nAdding (1) and (2), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118163\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-18.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 18.3\" width=\"155\" height=\"39\" \/><br \/>\nPutting x = 9 in (1), we get<br \/>\n9 &#8211; y = 7<br \/>\ny = 9 &#8211; 7<br \/>\ny = 2<br \/>\nx = 9, y = 2<br \/>\nHence, the required number = 9 \u00d7 10 + 2<br \/>\n= 92.<br \/>\n<span style=\"color: #993366;\"><strong>Question 19:<\/strong><\/span><br \/>\nLet the ten&#8217;s digit be x and the unit digit be y respectively.<br \/>\nThen, required number = 10x + y<br \/>\nAccording to the given question:<br \/>\n10x + y = 4(x + y)<br \/>\n6x &#8211; 3y = 0<br \/>\n2x &#8211; y = 0 &#8212;(1)<br \/>\nAnd<br \/>\n10x + y = 2xy &#8212;(2)<br \/>\nPutting y = 2x from (1) in (2), we get<br \/>\n10x + 2x = 4x<sup>2<\/sup>\u00a0\u21d2 12x &#8211; 4x<sup>2<\/sup> = 0\u00a0\u21d2 4x(3 &#8211; x) = 0\u00a0\u21d2 x = 3<br \/>\nPutting x = 3 in (1), we get<br \/>\n2 \u00d7 3 &#8211; y = 0<br \/>\ny = 6<br \/>\nHence, the required number = 3 \u00d7 10 + 6<br \/>\n= 36.<br \/>\n<span style=\"color: #993366;\"><strong>Question 20:<\/strong><\/span><br \/>\nLet the numerator and denominator of fraction be x and y respectively.<br \/>\nAccording to the question:<br \/>\nx + y = 8 &#8212;(1)<br \/>\nAnd<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118164\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-20.1.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 20.1\" width=\"131\" height=\"62\" \/><br \/>\nMultiplying (1) be 3 and (2) by 1<br \/>\n3x + 3y = 24 &#8212;(3)<br \/>\n4x &#8211; 3y = -3 &#8212;(4)<br \/>\nAdd (3) and (4), we get<br \/>\n\\(7x=21\\\\ x=\\frac { 21 }{ 7 } =3 \\)<br \/>\nPutting x = 3 in (1), we get<br \/>\n3 + y= 8<br \/>\ny = 8 &#8211; 3<br \/>\ny = 5<br \/>\nx = 3, y = 5<br \/>\nHence, the fraction is\u00a0\\(\\frac { x }{ y } =\\frac { 3 }{ 5 } \u00a0\\)<br \/>\n<span style=\"color: #993366;\"><strong>Question 21:<\/strong><\/span><br \/>\nLet numerator and denominator be x and y respectively.<br \/>\nSum of numerator and denominator = x + y<br \/>\n3 less than 2 times y = 2y &#8211; 3<br \/>\nx + y =2y &#8211; 3<br \/>\nor x &#8211; y = -3 &#8212;(1)<br \/>\nWhen 1 is decreased from numerator and denominator, the fraction becomes:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118165\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-21.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 21.1\" width=\"81\" height=\"41\" \/><br \/>\n2(x &#8211; 1) = y &#8211; 1<br \/>\nor 2x &#8211; 2 = y &#8211; 1<br \/>\nor 2x &#8211; y = 1 &#8212;(2)<br \/>\nSubtracting (1) from (2), we get<br \/>\nx = 1 + 3 = 4<br \/>\nPutting x = 4 in (1), we get<br \/>\ny = x + 3<br \/>\n= 4 + 3<br \/>\n= 7<br \/>\nthe fraction is \\(\\frac { x }{ y } =\\frac { 4 }{ 7 } \\)<br \/>\n<span style=\"color: #993366;\"><strong>Question 22:<\/strong><\/span><br \/>\nLet the numerator and denominator be x and y respectively.<br \/>\nThen the fraction is \\(\\frac { x\u00a0}{ y\u00a0} \\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118166\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-22.1.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 22.1\" width=\"310\" height=\"63\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-22.1.jpg 310w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-22.1-300x61.jpg 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><br \/>\nSubtracting (1) from (2), we get<br \/>\nx = 15<br \/>\nPutting x = 15 in (1), we get<br \/>\n2 \u00d7 15 &#8211; y = 4<br \/>\n30 &#8211; y = 4<br \/>\ny = 26<br \/>\nx = 15 and y = 26<br \/>\nHence the given fraction is \\(\\frac { 15 }{ 26 } \\)<br \/>\n<span style=\"color: #993366;\"><strong>Question 23:<\/strong><\/span><br \/>\nLet the numerator and denominator be x and y respectively.<br \/>\nThen the fraction is \\(\\frac { x\u00a0}{ y\u00a0} \\).<br \/>\nAccording to the given question:<br \/>\ny = x + 11<br \/>\ny &#8211; x = 11 &#8212;(1)<br \/>\nand<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118167\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-23.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 23.1\" width=\"328\" height=\"41\" \/><br \/>\n-3y + 4x = -8 &#8212;(2)<br \/>\nMultiplying (1) by 4 and (2) by 1<br \/>\n4y &#8211; 4x = 44 &#8212;(3)<br \/>\n-3y + 4x = -8 &#8212;(4)<br \/>\nAdding (3) and (4), we get<br \/>\ny = 36<br \/>\nPutting y = 36 in (1), we get<br \/>\ny &#8211; x = 11<br \/>\n36 &#8211; x = 11<br \/>\nx = 25<br \/>\nx = 25, y = 36<br \/>\nHence the fraction is\u00a0\\(\\frac { 25 }{ 36 } \\)<br \/>\n<span style=\"color: #993366;\"><strong>Question 24:<\/strong><\/span><br \/>\nLet the numerator and denominator be x and y respectively.<br \/>\nThen the fraction is \\(\\frac { x\u00a0}{ y\u00a0} \\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118168\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-24.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 24.1\" width=\"343\" height=\"85\" \/><br \/>\nSubtracting (1) from (2), we get<br \/>\nx = 3<br \/>\nPutting x = 3 in (1), we get<br \/>\n2 \u00d7 3 &#8211; 4<br \/>\n-y = -4 -6<br \/>\ny = 10<br \/>\nx = 3 and y = 10<br \/>\nHence the fraction is\u00a0\\(\\frac { 3\u00a0}{ 10\u00a0} \\)<br \/>\n<span style=\"color: #993366;\"><strong>Question 25:<\/strong><\/span><br \/>\nLet the fraction be \\(\\frac { x\u00a0}{ y\u00a0} \\).<br \/>\nWhen 2 is added to both the numerator and the denominator, the fraction becomes:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118169\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-25.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 25.1\" width=\"213\" height=\"41\" \/><br \/>\n3x &#8211; y = -4 &#8212;(1)<br \/>\nWhen 3 is added both to the numerator and the denominator, the fractions becomes:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118170\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-25.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 25.2\" width=\"223\" height=\"41\" \/><br \/>\n5x &#8211; 2y = -9 &#8212;-(2)<br \/>\nMultiplying (1) by 2 and (2) by 1, we get<br \/>\n6x &#8211; 2y = -8 &#8212;(3)<br \/>\n5x &#8211; 2y = -9 &#8212;(4)<br \/>\nSubtracting (4) from (3), we get<br \/>\nx = 1<br \/>\nPutting x = 1 in (1),<br \/>\n3 \u00d7 1 &#8211; y = 4<br \/>\ny = 7<br \/>\nRequired fraction is\u00a0\\(\\frac { 1\u00a0}{ 7\u00a0} \\)<br \/>\n<span style=\"color: #993366;\"><strong>Question 26:<\/strong><\/span><br \/>\nLet the two numbers be x and y respectively.<br \/>\nAccording to the given question:<br \/>\nx + y = 16 &#8212;(1)<br \/>\nAnd<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118171\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-26.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 26.1\" width=\"72\" height=\"41\" \/>&#8212;(2)<br \/>\nFrom (2),<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118172\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-26.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 26.2\" width=\"249\" height=\"41\" \/><br \/>\nxy = 48<br \/>\nWe know,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118175\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-26.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 26.3\" width=\"284\" height=\"81\" \/><br \/>\nAdding (1) and (3), we get<br \/>\n2x = 24<br \/>\nx = 12<br \/>\nPutting x = 12 in (1),<br \/>\ny = 16 &#8211; x<br \/>\n= 16 &#8211; 12<br \/>\n= 4<br \/>\nThe required numbers are 12 and 4.<br \/>\n<span style=\"color: #993366;\"><strong>Question 27:<\/strong><\/span><br \/>\nLet the present ages of the man and his son be x years and y years respectively.<br \/>\nThen,<br \/>\nTwo years ago:<br \/>\n(x &#8211; 2) = 5(y &#8211; 2)<br \/>\nx &#8211; 2 = 5y &#8211; 10<br \/>\nx &#8211; 5y = -8 &#8212;(1)<br \/>\nTwo years later:<br \/>\n(x + 2) = 3(y + 2) + 8<br \/>\nx + 2 = 3y + 6 + 8<br \/>\nx &#8211; 3y = 12 &#8212;(2)<br \/>\nSubtracting (2) from (1), we get<br \/>\n-2y = -20<br \/>\ny = 10<br \/>\nPutting y = 10 in (1), we get<br \/>\nx &#8211; 5 \u00d7 10 = -8<br \/>\nx &#8211; 50 = -8<br \/>\nx = 42<br \/>\nHence the present ages of the man and the son are 42 years and 10 respectively.<br \/>\n<span style=\"color: #993366;\"><strong>Question 28:<\/strong><\/span><br \/>\nLet the present ages of A and B be x and y respectively.<br \/>\nFive years ago:<br \/>\n(x &#8211; 5) = 3(y &#8211; 5)<br \/>\nx &#8211; 5 = 3y &#8211; 15<br \/>\nx &#8211; 3y = -10 &#8212;(1)<br \/>\nTen years later:<br \/>\n(x + 10) = 2(y + 10)<br \/>\nx + 10 = 2y + 20<br \/>\nx &#8211; 2y = 10 &#8212;(2)<br \/>\nSubtracting (2) from (1), we get<br \/>\ny = 20<br \/>\nPutting y = 20 in (1), we get<br \/>\nx &#8211; 3y = -10<br \/>\nx &#8211; 3 \u00d7 20 = -10<br \/>\nx = -10 + 60 = 50<br \/>\nx = 50, y = 20<br \/>\nHence, present ages of A and B are 50 years and 20 years respectively.<br \/>\n<span style=\"color: #993366;\"><strong>Question 29:<\/strong><\/span><br \/>\nLet the present ages of woman and daughter be x and y respectively.<br \/>\nThen,<br \/>\nTheir present ages:<br \/>\nx = 3y + 3<br \/>\nx &#8211; 3y = 3 &#8212;(1)<br \/>\nThree years later:<br \/>\n(x + 3) = 2(y + 3) + 10<br \/>\nx + 3 = 2y + 6 + 10<br \/>\nx &#8211; 2y = 13 &#8212;(2)<br \/>\nSubtracting (2) from (1), we get<br \/>\ny = 10<br \/>\nPutting y = 10 in (1), we get<br \/>\nx &#8211; 3 \u00d7 10 = 3<br \/>\nx = 33<br \/>\nx = 33, y = 10<br \/>\nHence, present ages of woman and daughter are 33 and 10 years.<br \/>\n<span style=\"color: #993366;\"><strong>Question 30:<\/strong><\/span><br \/>\nLet the present ages of the mother and her son be x and y respectively.<br \/>\nAccording to the given question:<br \/>\nx + 2y = 70 &#8212;(1)<br \/>\nand<br \/>\n2x + y = 95 &#8212;(2)<br \/>\nMultiplying (1) by 1 and (2) by 2, we get<br \/>\nx + 2y = 70 &#8212;(3)<br \/>\n4x + 2y = 190 &#8212;(4)<br \/>\nSubtracting (3) from (4), we get<br \/>\n\\(3x=120\\\\ y=\\frac { 120 }{ 3\u00a0} =40 \\)<br \/>\nPutting x = 40 in (1), we get<br \/>\n40 + 2y = 70<br \/>\n2y = 30<br \/>\ny = 15<br \/>\nx = 40, y = 15<br \/>\nHence, the ages of the mother and the son are 40 years and 15 years respectively.<br \/>\n<span style=\"color: #993366;\"><strong>Question 31:<\/strong><\/span><br \/>\nLet the present age of the man and the sum of the ages of the two sons be x and y respectively.<br \/>\nWe are given x = 3y &#8212;(1)<br \/>\nAfter 5 years the age of man = x + 5<br \/>\nAnd age of each son is increased by 5 years<br \/>\nAge of two sons after 5 years = y + 5 + 5 = y + 10<br \/>\nNow,<br \/>\nx + 5 = 2(y + 10)<br \/>\nor x + 5 = 2y + 10<br \/>\nx &#8211; 2y = 15 &#8212;(2)<br \/>\nPutting x = 3y in (2)<br \/>\n3y &#8211; 2y = 15<br \/>\ny = 15<br \/>\nPutting y = 15 in (1),<br \/>\nx = 3 \u00d7 15 = 45<br \/>\nAge of the man = 45 years.<br \/>\n<span style=\"color: #993366;\"><strong>Question 32:<\/strong><\/span><br \/>\nLet the present age of the man and his son be x and y respectively.<br \/>\nTen years later:<br \/>\n(x + 10) = 2(y + 10)<br \/>\nx + 10 = 2y + 20<br \/>\nx &#8211; 2y = 10 &#8212;(1)<br \/>\nTen years ago:<br \/>\n(x &#8211; 10) = 4(y &#8211; 10)<br \/>\nx &#8211; 10 = 4y &#8211; 40<br \/>\nx &#8211; 4y = &#8211; 30 &#8212;(2)<br \/>\nSubtracting (1) from (2), we get<br \/>\n-2y = -40<br \/>\ny = 20 years<br \/>\nPutting y = 20 in (1), we get<br \/>\nx &#8211; 2 \u00d7 20 = 10<br \/>\nx = 50<br \/>\nx = 50 years, y = 20 years<br \/>\nHence, present ages of the man and his son are 50 years and 20 years respectively.<br \/>\n<span style=\"color: #993366;\"><strong>Question 33:<\/strong><\/span><br \/>\nLet the monthly income of A and B be Rs. 5x and Rs. 4x respectively and let their expenditures be Rs. 7y and Rs. 5y respectively.<br \/>\nThen,<br \/>\n5x &#8211; 7y = 3000 &#8212;(1)<br \/>\n4x &#8211; 5y = 3000 &#8212;(2)<br \/>\nMultiplying (1) by 5 and (2) by 7 we get<br \/>\n25x &#8211; 35y = 15000 &#8212;(3)<br \/>\n28x &#8211; 35y = 21000 &#8212;(4)<br \/>\nSubtracting (3) from (4), we get<br \/>\n3x = 6000<br \/>\nx = 2000<br \/>\nPutting x = 2000 in (1), we get<br \/>\n5 \u00d7 2000 &#8211; 7y = 3000<br \/>\n-7y = 3000 &#8211; 10000<br \/>\n\\(y=\\frac { -7000 }{ -7 } =1000 \\)<br \/>\nx = 2000, y = 1000<br \/>\nIncome of A = 5x = 5 \u00d7 2000 = Rs. 10000<br \/>\nIncome of B = 4x = 4 \u00d7 2000 = Rs. 8000<br \/>\n<span style=\"color: #993366;\"><strong>Question 34:<\/strong><\/span><br \/>\nLet Rs. x and Rs. y be the CP of a chair and table respectively<br \/>\nIf profit is 25%, then SP of chair =<img loading=\"lazy\" class=\"alignnone size-full wp-image-118176\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.1.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 34.1\" width=\"152\" height=\"28\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.1.jpg 152w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.1-150x28.jpg 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><br \/>\nIf profit is 10%, then SP of the table =<img loading=\"lazy\" class=\"alignnone size-full wp-image-118177\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.2.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 34.2\" width=\"154\" height=\"28\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.2.jpg 154w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.2-150x28.jpg 150w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><br \/>\nSP of a chair and table = Rs. 760<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118178\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.3.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 34.3\" width=\"173\" height=\"80\" \/><br \/>\nFurther , If profit is 10%, then SP of a chair =<img loading=\"lazy\" class=\"alignnone size-full wp-image-118179\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.4.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 34.4\" width=\"100\" height=\"28\" \/>\\(Rs\\frac { 110 }{ 100 } x \\)<br \/>\nIf profit is 25%, then SP of a table =<img loading=\"lazy\" class=\"alignnone size-full wp-image-118180\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.5.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 34.5\" width=\"101\" height=\"28\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.5.jpg 101w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.5-100x28.jpg 100w\" sizes=\"(max-width: 101px) 100vw, 101px\" \/>\\(Rs\\frac { 125 }{ 100 } y \\)<br \/>\nSP of a chair and table = Rs. 767.50<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118181\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.6.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 34.6\" width=\"174\" height=\"80\" \/><br \/>\nAdding (1) and (2),<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118182\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.7.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 34.7\" width=\"256\" height=\"64\" \/><br \/>\nSubtracting (2) from (1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118183\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.8.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 34.8\" width=\"147\" height=\"56\" \/><br \/>\nAdding (3) and (4),<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118184\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.9.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 34.9\" width=\"95\" height=\"62\" \/><br \/>\nSubtracting (4) from (3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118185\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-34.10.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 34.10\" width=\"95\" height=\"62\" \/><br \/>\nHence, CP of a chair is Rs 300 and CP of table is Rs 350.<br \/>\n<span style=\"color: #993366;\"><strong>Question 35:<\/strong><\/span><br \/>\nLet the CP of TV and fridge be Rs x and Rs y respectively.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118186\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-35.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 35.1\" width=\"350\" height=\"216\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-35.1.png 350w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-35.1-300x185.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><br \/>\nFurther,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118187\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-35.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 35.2\" width=\"226\" height=\"145\" \/><br \/>\n2x &#8211; y = 30000 &#8212;(2)<br \/>\nMultiplying (2) by 2 and (1) by 1, we get<br \/>\n4x &#8211; 2y = 60000 &#8212;(3)<br \/>\nx + 2y = 65000 &#8212;(4)<br \/>\nAdding (3) and (4), we get<br \/>\n5x = 125000<br \/>\nx = 25000<br \/>\nPutting x = 25000 in (1), we get<br \/>\n25000 + 2y = 65000<br \/>\n2y = 40000<br \/>\ny = 20000<br \/>\nThe cost of TV = Rs. 25000 and cost of fridge = Rs. 20000<br \/>\n<span style=\"color: #993366;\"><strong>Question 36:<\/strong><\/span><br \/>\nLet the amounts invested at 12% and 10% be Rs x and Rs y respectively.<br \/>\nThen,<br \/>\nFirst case:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118422\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-Q36.1.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Q36.1\" width=\"327\" height=\"224\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-Q36.1.png 327w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-Q36.1-300x206.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nSecond case:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118188\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-36.2.png\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 36.2\" width=\"388\" height=\"245\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-36.2.png 388w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-36.2-300x189.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><br \/>\nMultiplying (1) by 6 and (2) by 5, we get<br \/>\n36x + 30y = 343500 &#8212;(3)<br \/>\n25x + 30y = 263750 &#8212;(4)<br \/>\nSubtracting (4) from (3), we get<br \/>\n\\(11x=79750\\\\ x=\\frac { 79750 }{ 11 } =7250 \\)<br \/>\nPutting x = 7250 in (1), we get<br \/>\n6 \u00d7 7250 + 5y = 57250<br \/>\n43500 + 5y = 57250<br \/>\n5y = 13750<br \/>\ny = 2750<br \/>\nx = 7250, y = 2750<br \/>\nHence, amount invested at 12% = Rs 7250<br \/>\nAnd amount invested at 10% = Rs 2750<br \/>\n<span style=\"color: #993366;\"><strong>Question 37:<\/strong><\/span><br \/>\nLet the number of student in class room A and B be x and y respectively.<br \/>\nWhen 10 students are transferred from A to B:<br \/>\nx &#8211; 10 = y + 10<br \/>\nx &#8211; y = 20 &#8212;(1)<br \/>\nWhen 20 students are transferred from B to A:<br \/>\n2(y &#8211; 20) = x + 20<br \/>\n2y &#8211; 40 = x + 20<br \/>\n-x + 2y = 60 &#8212;(2)<br \/>\nAdding (1) and (2), we get<br \/>\ny = 80<br \/>\nPutting y = 80 in (1), we get<br \/>\nx &#8211; 80 = 20<br \/>\nx = 100<br \/>\nHence, number of students of A and B are 100 and 80 respectively.<br \/>\n<span style=\"color: #993366;\"><strong>Question 38:<\/strong><\/span><br \/>\nLet P and Q be the cars starting from A and B respectively and let their speeds be x km\/hr and y km\/hr respectively.<br \/>\nCase- I<br \/>\nWhen the cars P and Q move in the same direction.<br \/>\nDistance covered by the car P in 7 hours = 7x km<br \/>\nDistance covered by the car Q in 7 hours = 7y km<br \/>\nLet the cars meet at point M.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118189\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-38.1.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 38.1\" width=\"452\" height=\"50\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-38.1.jpg 452w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-38.1-300x33.jpg 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><br \/>\nAM = 7x km and BM = 7y km<br \/>\nAM &#8211; BM = AB<br \/>\n7x &#8211; 7y = 70<br \/>\n7(x &#8211; y) = 70<br \/>\nx &#8211; y = 10 &#8212;-(1)<br \/>\nCase II<br \/>\nWhen the cars P and Q move in opposite directions.<br \/>\nDistance covered by P in 1 hour = x km<br \/>\nDistance covered by Q in 1 hour = y km<br \/>\nIn this case let the cars meet at a point N.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118190\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-38.2.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 38.2\" width=\"372\" height=\"38\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-38.2.jpg 372w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-38.2-300x31.jpg 300w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><br \/>\nAN = x km and BN = y km<br \/>\nAN + BN = AB<br \/>\nx + y = 70 &#8212;(2)<br \/>\nAdding (1) and (2), we get<br \/>\n2x = 80<br \/>\nx = 40<br \/>\nPutting x = 40 in (1), we get<br \/>\n40 &#8211; y = 10<br \/>\ny = (40 &#8211; 10) = 30<br \/>\nx = 40, y = 30<br \/>\nHence, the speeds of these cars are 40 km\/ hr and 30 km\/ hr respectively.<br \/>\n<span style=\"color: #993366;\"><strong>Question 39:<\/strong><\/span><br \/>\nLet the original speed be x km\/h and time taken be y hours<br \/>\nThen, length of journey = xy km<br \/>\nCase I:<br \/>\nSpeed = (x + 5)km\/h and time taken = (y &#8211; 3)hour<br \/>\nDistance covered = (x + 5)(y &#8211; 3)km<br \/>\n(x + 5) (y &#8211; 3) = xy<br \/>\nxy + 5y -3x -15 = xy<br \/>\n5y &#8211; 3x = 15 &#8212;(1)<br \/>\nCase II:<br \/>\nSpeed (x &#8211; 4)km\/hr and time taken = (y + 3)hours<br \/>\nDistance covered = (x &#8211; 4)(y + 3) km<br \/>\n(x &#8211; 4)(y + 3) = xy<br \/>\nxy -4y + 3x -12 = xy<br \/>\n3x &#8211; 4y = 12 &#8212;(2)<br \/>\nMultiplying (1) by 4 and (2) by 5, we get<br \/>\n20y \u00d7 12x = 60 &#8212;(3)<br \/>\n-20y + 15x = 60 &#8212;(4)<br \/>\nAdding (3) and (4), we get<br \/>\n3x = 120<br \/>\nor x = 40<br \/>\nPutting x = 40 in (1), we get<br \/>\n5y &#8211; 3 \u00d7 40 = 15<br \/>\n5y = 135<br \/>\ny = 27<br \/>\nHence, length of the journey is (40 \u00d7 27) km = 1080 km<br \/>\n<span style=\"color: #993366;\"><strong>Question 40:<\/strong><\/span><br \/>\nLet the speed of train and car be x km\/hr and y km\/hr respectively.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118191\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-40.1.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 40.1\" width=\"206\" height=\"246\" \/><br \/>\nMultiplying (1) by 40 and (2) by 1, we get<br \/>\n5000u + 2400v = 80 &#8212;(3)<br \/>\n1300u + 2400v = 43 &#8212;(4)<br \/>\nsubtracting (4) from (3), we get<br \/>\n\\(3700u=37\\\\ u=\\frac { 1 }{ 100 } \\)<br \/>\nPutting \\(u=\\frac { 1 }{ 100 } \u00a0\\) in (1), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118192\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-40.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 40.2\" width=\"375\" height=\"121\" \/><br \/>\nHence, speeds of the train and the car are 100km\/hr and 80 km\/hr respectively.<br \/>\n<span style=\"color: #993366;\"><strong>Question 41:<\/strong><\/span><br \/>\nLet the speed of the boat in still water be x km\/hr and speed of the stream be y km\/hr.<br \/>\nThen,<br \/>\nSpeed upstream = (x &#8211; y)km\/hr<br \/>\nSpeed downstream = (x + y) km\/hr<br \/>\nTime taken to cover 12 km upstream = \\(\\frac { 12 }{ x-y } hrs \u00a0\\)<br \/>\nTime taken to cover 40 km downstream = \\(\\frac { 40 }{ x+y } hrs \u00a0\\)<br \/>\nTotal time taken = 8hrs<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118193\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-41.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 41.1\" width=\"136\" height=\"41\" \/><br \/>\nAgain, time taken to cover 16 km upstream = \\(\\frac { 16\u00a0}{ x-y } \u00a0\\)<br \/>\nTime taken to taken to cover 32 km downstream = \\(\\frac { 32 }{ x+y } \u00a0\\)<br \/>\nTotal time taken = 8hrs<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118194\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-41.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 41.2\" width=\"157\" height=\"44\" \/><br \/>\nPutting <img loading=\"lazy\" class=\"alignnone size-full wp-image-118195\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-41.3.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 41.3\" width=\"255\" height=\"44\" \/><br \/>\n12u + 40v = 8<br \/>\n3u + 10v = 2 &#8212;(1)<br \/>\nand<br \/>\n16u + 32v = 8<br \/>\n2u + 4v = 1 &#8212;(2)<br \/>\nMultiplying (1) by 4 and (2) by 10, we get<br \/>\n12u + 40v = 8 &#8212;(3)<br \/>\n20u + 40v = 10 &#8212;(4)<br \/>\nSubtracting (3) from (4), we get<br \/>\n\\(8u=2\\\\ u=\\frac { 1 }{ 4\u00a0} \\)<br \/>\nPutting \\(u=\\frac { 1 }{ 4\u00a0} \u00a0\\) in (3), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118196\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-41.4.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 41.4\" width=\"281\" height=\"124\" \/><br \/>\nOn adding (5) and (6), we get<br \/>\n2x = 12<br \/>\nx = 6<br \/>\nPutting x = 6 in (6) we get<br \/>\n6 + y = 8<br \/>\ny = 8 &#8211; 6 = 2<br \/>\nx = 6, y = 2<br \/>\nHence, the speed of the boat in still water = 6 km\/hr and speed of the stream = 2km\/hr<br \/>\n<span style=\"color: #993366;\"><strong>Question 42:<\/strong><\/span><br \/>\nLet the fixed charges of taxi per day be Rs x and charges for travelling for 1km be Rs y.<br \/>\nFor travelling 110 km, he pays<br \/>\nRs x + Rs 110y = Rs 1130<br \/>\nx + 110y = 1130 &#8212;(1)<br \/>\nFor travelling 200 km, he pays<br \/>\nRs x + Rs 200y = Rs 1850<br \/>\nx + 200y = 1850 &#8212;(2)<br \/>\nSubtracting (1) from (2), we get<br \/>\n\\(90y=1850-1130=720\\\\ y=\\frac { 720 }{ 90 } =8 \u00a0\\)<br \/>\nPutting y = 8 in (1),<br \/>\nx + 110 \u00d7 8 = 1130<br \/>\nx = 1130 &#8211; 880 = 250<br \/>\nHence, fixed charges = Rs 250<br \/>\nAnd charges for travelling 1 km = Rs 8<br \/>\n<span style=\"color: #993366;\"><strong>Question 43:<\/strong><\/span><br \/>\nLet the fixed hostel charges be Rs x and food charges per day be Rs y respectively.<br \/>\nFor student A:<br \/>\nStudent takes food for 25days and he has to pay: Rs 3500<br \/>\nRs x + Rs 25y = Rs 3500<br \/>\nx + 25y = 3500 &#8212;(1)<br \/>\nFor student B:<br \/>\nStudent takes food for 28days and he has to pay: Rs 3800<br \/>\nRs x + Rs 28y = Rs 3800<br \/>\nor x + 28y = 3800 &#8212;(2)<br \/>\nSubtracting (1) from (2), we get<br \/>\n3y = 3800 &#8211; 3500<br \/>\n3y= 300<br \/>\ny = 100<br \/>\nPutting y = 100 in (1),<br \/>\nx + 25 \u00d7 100 = 3500<br \/>\nor x = 3500 &#8211; 2500<br \/>\nor x = 1000<br \/>\nThus, fixed charges for hostel = Rs 1000 and<br \/>\nCharges for food per day = Rs 100<br \/>\n<span style=\"color: #993366;\"><strong>Question 44:<\/strong><\/span><br \/>\nLet the length = x meters and breadth = y meters<br \/>\nThen,<br \/>\nx = y + 3<br \/>\nx &#8211; y = 3 &#8212;-(1)<br \/>\nAlso,<br \/>\n(x + 3)(y &#8211; 2) = xy<br \/>\n3y &#8211; 2x = 6 &#8212;-(2)<br \/>\nMultiplying (1) by 2 and (2) by 1<br \/>\n-2y + 2x = 6 &#8212;(3)<br \/>\n3y &#8211; 2x = 6 &#8212;(4)<br \/>\nAdding (3) and (4), we get<br \/>\ny = 12<br \/>\nPutting y = 12 in (1), we get<br \/>\nx &#8211; 12 = 3<br \/>\nx = 15<br \/>\nx = 15, y = 12<br \/>\nHence length = 15 metres and breadth = 12 metres<br \/>\n<span style=\"color: #993366;\"><strong>Question 45:<\/strong><\/span><br \/>\nLet the length of a rectangle be x meters and breadth be y meters.<br \/>\nThen, area = xy sq.m<br \/>\nNow,<br \/>\nxy &#8211; (x &#8211; 5)(y + 3) = 8<br \/>\nxy \u00d7 [xy \u00d7 5y + 3x -15] = 8<br \/>\nxy \u00d7 xy + 5y \u00d7 3x + 15 = 8<br \/>\n3x &#8211; 5y = 7 &#8212;(1)<br \/>\nAnd<br \/>\n(x + 3)(y + 2) &#8211; xy = 74<br \/>\nxy + 3y +2x + 6 \u00d7 xy = 74<br \/>\n2x + 3y = 68 &#8212;(2)<br \/>\nMultiplying (1) by 3 and (2) by 5, we get<br \/>\n9x &#8211; 15y = 21 &#8212;(3)<br \/>\n10x + 15y = 340 &#8212;(4)<br \/>\nAdding (3) and (4), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118197\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-45.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 45.1\" width=\"191\" height=\"39\" \/><br \/>\nPutting x = 19 in (3) we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118198\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-45.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 45.2\" width=\"365\" height=\"39\" \/><br \/>\nx = 19 meters, y = 10 meters<br \/>\nHence, length = 19m and breadth = 10m<br \/>\n<span style=\"color: #993366;\"><strong>Question 46:<\/strong><\/span><br \/>\nLet man&#8217;s 1 day&#8217;s work be \\(\\frac { 1 }{ x } \u00a0\\) and 1 boy&#8217;s day&#8217;s work be \\(\\frac { 1 }{ y\u00a0} \u00a0\\)<br \/>\nAlso let \\(\\frac { 1 }{ x } =u \u00a0\\) and \\(\\frac { 1 }{ y\u00a0} =v \u00a0\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118199\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-46.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 46.1\" width=\"284\" height=\"85\" \/><br \/>\nMultiplying (1) by 6 and (2) by 5 we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118200\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-46.2.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 46.2\" width=\"168\" height=\"79\" \/><br \/>\nSubtracting (3) from (4), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118201\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-46.3.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 46.3\" width=\"93\" height=\"152\" \/><br \/>\nPutting \\(u=\\frac { 1 }{ 18\u00a0} \u00a0\\)\u00a0in (1), we get<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118202\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-46.4.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 46.4\" width=\"324\" height=\"179\" \/><br \/>\nx = 18, y = 36<br \/>\nThe man will finish the work in 18 days and the boy will finish the work in 36 days when they work alone.<br \/>\n<span style=\"color: #993366;\"><strong>Question 47:<\/strong><\/span><br \/>\n\u2220A +\u2220B + \u2220C = 180\u25e6<br \/>\nx + 3x + y = 180<br \/>\n4x + y = 180 &#8212;(1)<br \/>\nAlso,<br \/>\n3y &#8211; 5x = 30<br \/>\n-5x + 3y = 30 &#8212;(2)<br \/>\nMultiplying (1) by 3 and (2) by 1, we get<br \/>\n12x + 3y = 540 &#8212;(3)<br \/>\n-5x + 3y = 30 &#8212;(4)<br \/>\nSubtracting (4) from (3), we get<br \/>\n17x = 510<br \/>\nx = 30<br \/>\nPutting x = 30 in (1), we get<br \/>\n4 \u00d7 30 + y = 180<br \/>\ny = 60<br \/>\nHence \u2220A = 30\u25e6, \u2220B = 3 \u00d7 30\u25e6 = 90\u25e6, \u2220C = 60\u25e6<br \/>\nTherefore, the triangle is right angled.<br \/>\n<span style=\"color: #993366;\"><strong>Question 48:<\/strong><\/span><br \/>\nIn a cyclic quadrilateral ABCD:<br \/>\n\u2220A = (x + y + 10)\u00b0,<br \/>\n\u2220B = (y + 20)\u00b0,<br \/>\n\u2220C = (x + y &#8211; 30)\u00b0,<br \/>\n\u2220D = (x + y)\u00b0<br \/>\nWe have, \u2220A + \u2220C = 180\u00b0 and \u2220B + \u2220D = 180\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118203\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-48.1.gif\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 48.1\" width=\"203\" height=\"25\" \/><br \/>\nNow,<br \/>\n\u2220A + \u2220C = (x + y + 10)\u00b0 + (x + y &#8211; 30)\u00b0 = 180\u00b0<br \/>\n2x + 2y &#8211; 20\u00b0 = 180\u00b0<br \/>\nx + y &#8211; 10\u00b0 = 90\u00b0<br \/>\nx + y = 100 &#8212;(1)<br \/>\nAlso,<br \/>\n\u2220B + \u2220D = (y + 20)\u00b0 +(x + y)\u00b0 = 180\u00b0<br \/>\nx + 2y + 20\u00b0 = 180\u00b0<br \/>\nx + 2y = 160\u00b0 &#8212;(2)<br \/>\nSubtracting (1) from (2), we get<br \/>\ny = 160 &#8211; 100 = 60<br \/>\nPutting y = 60 in (1), we get<br \/>\nx = 100 &#8211; y<br \/>\nx = 100 &#8211; 60<br \/>\nx = 40<br \/>\nTherefore,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-118204\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-48.2.jpg\" alt=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables 3e 48.2\" width=\"336\" height=\"90\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-48.2.jpg 336w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/07\/RS-Aggarwal-Solutions-Class-10-Chapter-3-Linear-equations-in-two-variables-3e-48.2-300x80.jpg 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p>Hope given <a href=\"https:\/\/cbselibrary.com\/rs-aggarwal-solutions-class-10-chapter-3-linear-equations-in-two-variables\/\">RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables<\/a>\u00a0are helpful to complete your math homework.<\/p>\n<p>If you have any doubts, please comment below. <a href=\"https:\/\/cbselibrary.com\">A Plus Topper<\/a> try to provide online math tutoring for you.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Exercise 3A Question 1: h3 Read More: What is a Linear Equation Linear Equations In One Variable &#8230; <a title=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/rs-aggarwal-solutions-class-10-chapter-3-linear-equations-in-two-variables\/\" aria-label=\"More on RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6805],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/rs-aggarwal-solutions-class-10-chapter-3-linear-equations-in-two-variables\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables\" \/>\n<meta property=\"og:description\" content=\"RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables These Solutions are part of RS Aggarwal Solutions Class 10. 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