solve by elimination 6x-5y=22 and 9y+7=5x+8

Question

solve the system of equations by using the elimination method .
the equations are : 6x-5y=22 and 9y+7=5x+8

Answer 1

6x-5y = 22 ------> (1)

9y+7 = 5x+8

Subtract 5x,7 from each side.

9y-5x+7-7 = 5x-5x+8-7

9y-5x = 1

-5x+9y = 1------> (2)

Multiple to each side equation (1) by 5 and (2) by 6.

30x-25y = 110------->(3)

-30x+54y = 6 -------> (4)

To eliminate the x value add the equations (3) and (4).

30x-25y = 110

-30x+54y = 6

____________

29y =116

y = 116/29 = 4

Substitute the y value in (1).

6x-20 = 22

6x = 22+20

6x = 42

Divide to each side by 6.

6x/6  = 42/6

x  = 7

Solution x = 7,y = 4.