To solve this system of equations, you can use the method of substitution.
The first step is to solve one of the equations for one of the variables in terms of the other. You can start by solving the second equation for y:
5y - 8x = 10
y = (8x - 10) / 5
Next, you can substitute this expression for y in the first equation:
8((8x - 10) / 5) - 9x = -3
This simplifies to:
16x - 80 - 9x = -3
Which simplifies to:
7x - 80 = -3
Then, you can solve for x by adding 80 to both sides of the equation:
7x = 77
Finally, you can divide both sides of the equation by 7 to solve for x:
x = 11
Now that you have found the value of x, you can substitute it back into either of the original equations to find the value of y.
For example, you can substitute it into the second equation:
5y - 8(11) = 10
This simplifies to:
5y - 88 = 10
Then, you can solve for y by adding 88 to both sides of the equation:
5y = 98
Finally, you can divide both sides of the equation by 5 to solve for y:
y = 19.6
So, the solution to the system of equations is x = 11 and y = 19.6.