To solve the system of equations
- \(-3x - 4y = -23\)
- \(3x - 5y = 5\)
we can use the method of substitution or elimination. Let's use substitution in this case.
First, we can solve the second equation for \(x\):
\[ 3x - 5y = 5 \]
\[ 3x = 5 + 5y \]
\[ x = \frac{5 + 5y}{3} \]
Now, we can substitute this expression for \(x\) into the first equation:
\[ -3\left(\frac{5 + 5y}{3}\right) - 4y = -23 \]
This simplifies to:
\[ -(5 + 5y) - 4y = -23 \]
\[ -5 - 5y - 4y = -23 \]
\[ -5 - 9y = -23 \]
Adding 5 to both sides gives:
\[ -9y = -18 \]
Dividing by -9:
\[ y = 2 \]
Now we can substitute \(y = 2\) back into the expression for \(x\):
\[ x = \frac{5 + 5(2)}{3} \]
\[ x = \frac{5 + 10}{3} \]
\[ x = \frac{15}{3} = 5 \]
So the solution is:
\((x, y) = (5, 2)\).
Therefore, the correct response is:
\((5, 2)\).