Solution Of A Linear Equation In Two Variables

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Solution Of A Linear Equation In Two Variables Example Problems With Solutions

Method: Put the value of x (or y) = 0, ±1, ±2, ±3,……, we get values of y (or x). By this we can find many solutions of given equation.

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Example 1:    Find five solutions of
(i) 2x + 3y = 6          (ii) 3x – 2y = 12         (iii) 7x + y = 15
Solution:    (i) 2x = 6 – 3y
Solution Of A Linear Equation In Two Variables 1
Solution Of A Linear Equation In Two Variables 2

Example 2:    Find two solutions of
(i) 3x – 7y = 21 (ii) 8x – 5y = 16
Solution:    (i) 3x – 7y = 21
Solution Of A Linear Equation In Two Variables 3
Solution Of A Linear Equation In Two Variables 4

Example 3:    Find five solutions of
(i) 3x = 5             (ii) 7y = 10
Solution:    (i) The equation is only in one variable. So we have to convert into 2 variable 3x + 0.y = 5
Solution Of A Linear Equation In Two Variables 5
Note:
Ordered Pair: If value of x & y are represent in form (x, y) then this form is called ordered pair form : Eg. x = 5, y = 7/3 then ordered pair form = (5, 7/3). First part is called abscissa (x part) and second part is ordinate (y part).

Example 4:    Check the following value of x & y are solution of equation 9x – 8y = 72 or not
(i) (0, 9)               (ii) (0, – 9)               (iii) (– 8, 0)
(iv) (+8, 0)           (v) (1, 1)                    (vi) (1/3, 1/2)
Solution:    Given equation 9x – 8y = 72
Solution Of A Linear Equation In Two Variables 6

Example 5:    Find the value of k in equation 2x + ky = 6 if (–2, 2) is a solution.
Solution:    ∵ (–2, 2) is a solution of 2x + ky = 5
∴ 2(–2) + k(2) = 6
– 4 + 2k = 6 ⇒ 2k = 6 + 4
k = 10/2 = 5

Example 6:    Find value of p if (4, –4) is a solution of x – py = 8.
Solution:    x – py = 8
4 – p (–4) = 8
4p = 8 – 4
4p = 4
p = 1

Example 7:    Find the value of a if (a, –3a) is a solution of 14x + 3y = 35.
Solution:    Put x = a and y = –3a in given equation
14(a) + 3(–3a) = 35
14a – 9a = 35
5a = 35
a = 7

 

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