To solve the system of equations:
- \(-3x - 4y = -23\)
- \(3x - 5y = 5\)
We can use either substitution or elimination. Here, I'll use the elimination method.
First, let's align both equations:
- \(-3x - 4y = -23\)
- \(3x - 5y = 5\)
Next, we'll add the two equations together to eliminate \(x\). To do this, we can multiply the second equation by 1 and add:
\[ -3x - 4y + (3x - 5y) = -23 + 5 \]
This simplifies to:
\[ -4y - 5y = -18 \] \[ -9y = -18 \]
Now, solve for \(y\):
\[ y = \frac{-18}{-9} = 2 \]
Now that we have \(y = 2\), we can substitute \(y\) back into one of the original equations to find \(x\). We'll use the second equation:
\[ 3x - 5(2) = 5 \] \[ 3x - 10 = 5 \] \[ 3x = 15 \] \[ x = 5 \]
Thus, the solution to the system of equations is \((5, 2)\).
So the answer is:
(5, 2).