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