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

Let's use the elimination method. We can start by multiplying the first equation by 5 and the second equation by 9 to make the coefficients of either x or y the same in both equations:

5(8x - 9y) = 5(76)
9(6x + 5y) = 9(-37)

Simplifying, we get:
40x - 45y = 380
54x + 45y = -333

Now, we can add these two equations together to eliminate y:
40x - 45y + 54x + 45y = 380 - 333
94x = 47
x = 47/94
x = 0.5

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:

8(0.5) - 9y = 76
4 - 9y = 76
-9y = 72
y = -8

Therefore, the solution to the system of equations is x = 0.5 and y = -8.