To solve the given system of equations:
- \(-5x + 4y = 48\) (Equation 1)
- \(-5x - 8y = 24\) (Equation 2)
We can solve this system using the elimination method.
First, let's manipulate the equations to eliminate \(x\). We can subtract Equation 2 from Equation 1.
Subtracting Equation 2 from Equation 1:
\[ (-5x + 4y) - (-5x - 8y) = 48 - 24 \]
This simplifies to:
\[ 4y + 8y = 48 - 24 \]
\[ 12y = 24 \]
Now, divide both sides by 12:
\[ y = 2 \]
Now that we have \(y\), we can substitute it back into one of the original equations to find \(x\). Let's use Equation 1:
\(-5x + 4(2) = 48\)
This simplifies to:
\(-5x + 8 = 48\)
Now, subtract 8 from both sides:
\(-5x = 40\)
Now, divide by -5:
\[ x = -8 \]
So, the solution to the system is:
\((x, y) = (-8, 2)\)
The correct response is \((-8, 2)\).