To solve the system of equations:
- Equation 1: \(-3x - 4y = -23\)
- Equation 2: \(3x - 5y = 5\)
We can use the method of substitution or elimination. Here, I will use the elimination method.
First, let's multiply Equation 1 by -1 to make the coefficients of \(x\) in both equations opposites:
\[ 3x + 4y = 23 \quad \text{(Equation 3)} \]
Now we have:
- Equation 3: \(3x + 4y = 23\)
- Equation 2: \(3x - 5y = 5\)
Next, we can subtract Equation 2 from Equation 3 to eliminate \(x\):
\[ (3x + 4y) - (3x - 5y) = 23 - 5 \]
This simplifies to:
\[ 4y + 5y = 18 \] \[ 9y = 18 \]
Now, solve for \(y\):
\[ y = \frac{18}{9} = 2 \]
Now that we have the value of \(y\), we can substitute it back into one of the original equations to find \(x\). We'll use Equation 2:
\[ 3x - 5(2) = 5 \]
This simplifies to:
\[ 3x - 10 = 5 \]
Now, add 10 to both sides:
\[ 3x = 15 \]
Now divide by 3:
\[ x = 5 \]
Thus, the solution to the system of equations is:
\[ \boxed{(5, 2)} \]