To solve this system of equations, we will use the method of substitution or elimination.
Given equations:
1. -3x - 4y = -23
2. 3x - 5y = 5
First, we simplify equation 1 by multiplying by -1 to make the y coefficients match:
3x + 4y = 23
Next, we will add equation 1 and equation 2 to eliminate the x variable:
-3x - 4y + 3x - 5y = -23 + 5
-9y = -18
y = 2
Now, we substitute the value of y back into either equation 1 or equation 2 to solve for x:
3x - 5(2) = 5
3x - 10 = 5
3x = 15
x = 5
Therefore, the solution to the system of equations is x = 5 and y = 2.