Question

Solve :
11(x - 5) + 10(y - 2) + 54 = 0
7(2x - 1) + 9(3y - 1) = 25

Answer 1

11( x - 5 ) + 10( y - 2 ) + 54 = 0             (given)
⇒ 11x - 55 + 10y - 20 + 54 = 0
⇒ 11x + 10y - 21 = 0
⇒ 11x + 10y = 21                                 ....(1)

7( 2x - 1 ) + 9(3y - 1) = 25                     (given)
⇒ 14x - 7 + 27y - 9 = 25
⇒ 14x + 27y - 16 = 25
⇒ 14x + 27y = 41                               .....(2)

Multiplying equation (1) by 27 and equation (2) by 10, we get,
297x + 270y = 567                            ....(3)
140x + 270y = 410                            .....(4)

Subtracting equation (4) from equation (3), we get
157x = 157
⇒ x = 1

Substituting x = 1 in equation (1), we get,
11 x 1 + 10y = 21
⇒  10y = 10
⇒  y = 1
∴ Solution set is x = 1 and y = 1.