Q. 5

# Solve for x and y:3x - 5y - 19 = 0, - 7x + 3y + 1 = 0.

Rearranging the equations, we have

3x – 5y = 19    (1)

- 7x + 3y = - 1    (2)

To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.

Lets multiply (1) by 7 and (2) by 3, so that variable x in both the equations have same coefficient.

(3x – 5y = 19)×7

(-7x + 3y = - 1)×3

21x - 35y = 133    (3)
-21x + 9y = -3     (4)

adding (3) and (4), we get

-26y = 130

y = - 5

Substitute y = - 5 in (1)
3x - 5(-5) = 19
⇒ 3x + 25 = 19
⇒ 3x = -6
⇒ x = -2
Hence, x = -2 and y = -5 is the solution of given pair of equations.

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