Since we have the equations starting with 4x and -4x, it looks like we can combine them straight off and eliminate x:

-4x + 2y = 8
4x - 3y = -10

-y = -2    ====> y = 2

Plugging into either equation,

-4x + 2(2) = 8   ===>  -4x + 4 = 8    ===>  -4x = 4

x = -1

So our solution is (-1, 2)