Eliminate x by multiplying the top equation by -2.
-8x - 6y = -30
8x + 9y = 15
Adding the above two together gives us:
3y = -15
y = -5
Substitute this value of y into either equation to solve for x.
4x + 3(-5) = 15
4x - 15 = 15
4x = 30
x = 30/4 = 15/2