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

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

8x - y = -15
=> y = 8x + 15

Now we substitute this expression for y into the second equation:

x + 8*(8x + 15) = -10
x + 64x + 120 = -10
65x + 120 = -10
65x = -130
x = -130/65
x = -2

Now that we have found the value of x, we can substitute it back into the first equation to find the value of y:

8*(-2) - y = -15
-16 - y = -15
y = -15 + 16
y = 1

Therefore, the solution to the system of equations is x = -2 and y = 1.