To solve the system of equations using the elimination method, we start with the two equations:
- \(-3x - 4y = -23\) (Equation 1)
- \(3x - 5y = 5\) (Equation 2)
First, we can add the two equations together to eliminate the \(x\) variable. To do this, we can first manipulate the equations slightly:
- Multiply Equation 2 by \(1\):
\[ 3x - 5y = 5 \]
- Leave Equation 1 as is:
\[ -3x - 4y = -23 \]
Now, if we add both equations together, \(3x\) and \(-3x\) will cancel out:
\[ (-3x - 4y) + (3x - 5y) = -23 + 5 \]
This simplifies to:
\[ -4y - 5y = -23 + 5 \] \[ -9y = -18 \]
Now divide both sides by \(-9\):
\[ y = 2 \]
Now that we have \(y\), substitute \(y = 2\) back into either equation. We'll use Equation 2:
\[ 3x - 5(2) = 5 \] \[ 3x - 10 = 5 \]
Next, add 10 to both sides:
\[ 3x = 15 \] \[ x = 5 \]
The solution to the system of equations is:
\((x, y) = (5, 2)\)
Therefore, the correct response is:
(5, 2).