So the easiest method for this problem would be elimination. This is what you do...
-7x - 6y = 59
-1( -8x - 6y = 58)
New equations...
-7x - 6y = 59
8x + 6y = 58 (Add equations)
---------------------
1x = 1
Divide
x = 1
Now find the y value.
-7(1) - 6y = 59
-7 - 6y = 59
Add 7 to both sides.
-6y = 66
Divide
y = -11
So your solution is ( 1, -11)
I hope this helps love! :)