To solve the system of equations:
\[ -3x - 4y = -23 \quad \text{(1)} \] \[ 3x - 5y = 5 \quad \text{(2)} \]
We'll use the method of substitution or elimination. Here, I'll use the elimination method.
First, let's multiply equation (2) by 1 to keep it as it is:
\[ 3x - 5y = 5 \quad \text{(2)} \]
Now, we can add equations (1) and (2) by eliminating \(x\). However, it's better to multiply equation (1) by -1 so we can eliminate \(x\):
- From equation (1): \[ 3x + 4y = 23 \quad \text{(3)} \]
Now we have: \[ 3x + 4y = 23 \quad \text{(3)} \] \[ 3x - 5y = 5 \quad \text{(2)} \]
Now subtract equation (2) from equation (3):
\[ (3x + 4y) - (3x - 5y) = 23 - 5 \]
This simplifies to:
\[ 4y + 5y = 18 \] \[ 9y = 18 \]
Now solve for \(y\):
\[ y = \frac{18}{9} = 2 \]
Next, substitute \(y = 2\) back into one of the original equations to find \(x\). We'll use equation (2):
\[ 3x - 5(2) = 5 \] \[ 3x - 10 = 5 \] \[ 3x = 15 \] \[ x = 5 \]
So the solution to the system of equations is:
\[ (x, y) = (5, 2) \]
The answer is \((5, 2)\).