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

re-word the second equation:

9y +7 = 5x +8

9y -5x = 8 -7

-5x +9y = 1

now look at the equations together:

6x -5y = 22

-5x +9y = 1

multiply the top equation by 5

30x -25y = 110

-5x +9y = 1

multiply the bottom equation by 6

30x -25y = 110

-30x +54y = 6

add the equations together

0x +29y = 116

29y = 116

y = 116/29

y = 4

you could plug the y = 4 into one of the equations to get x, but that would be like substitution, so let's do this:

we had this:

6x -5y = 22

-5x +9y = 1

multiply the top equation by 9

54x -45y = 198

-5x +9y = 1

multiply the bottom equation by 5

54x -45y = 198

-25x +45y = 5

add the equations together

29x +0y = 203

29x = 203

x = 203/29

x = 7

Answer:  x = 7, y = 4