To solve the system of equations:
4m - 5n = 32
m + 2n = -5
We can use the method of substitution or elimination. Let's use the method of elimination.
1. Multiply the second equation by 4 to make the coefficients of m in both equations the same:
4m - 5n = 32
4m + 8n = -20
2. Subtract the first equation from the second equation:
(4m + 8n) - (4m - 5n) = -20 - 32
13n = -52
3. Divide both sides of the equation by 13:
n = -52 / 13
n = -4
4. Substitute the value of n = -4 into either of the original equations:
m + 2(-4) = -5
m - 8 = -5
m = -5 + 8
m = 3
Therefore, the solution to the system of equations is m = 3 and n = -4.