To solve this system of equations, we can use the method of substitution or elimination. Let's solve using substitution:

First, let's solve the second equation for y:

-2x + y = -8
y = 2x - 8

Now, substitute y = 2x - 8 into the first equation:

9x + 4(2x - 8) = -2
9x + 8x - 32 = -2
17x - 32 = -2
17x = 30
x = 30 / 17
x = 30/17

Now, substitute x back into the second equation to solve for y:

-2(30/17) + y = -8
-60/17 + y = -8
y = -8 + 60/17
y = -136/17 + 60/17
y = -76/17

Therefore, the solution to the system of equations is x = 30/17 and y = -76/17.