5x+8y=27, -5x-5y=-15
Combine the equations together.
5x + 8y = 27
-5x - 5y = -15
---------------------- add
3y = 12 iff
y = 4
Plug in y = 4 into any of the two equations to find x.
5x + 8y = 27
5x + 8(4) = 27 iff
5x + 32 = 27 iff
5x = -5 iff
x = -1
Thus the solution to the system is (-1, 4)