To solve the system of equations using elimination, we'll first write the equations:
- \(-4x - 2y = -12\)
- \(4x + 8y = -24\)
Next, we can manipulate the equations to eliminate one variable. In this case, we can try to eliminate \(x\) by adding both equations together.
First, let's align the equations:
\[
-4x - 2y = -12 \quad \text{(Equation 1)}
\]
\[
4x + 8y = -24 \quad \text{(Equation 2)}
\]
Now, add Equation 1 and Equation 2 together:
\[ (-4x - 2y) + (4x + 8y) = -12 + (-24) \]
This simplifies to:
\[ (-4x + 4x) + (-2y + 8y) = -36 \]
\[ 0x + 6y = -36 \]
Thus, we have:
\[ 6y = -36 \]
Now, solve for \(y\):
\[ y = \frac{-36}{6} \]
\[ y = -6 \]
Now that we have the value of \(y\), we can substitute it back into one of the original equations to solve for \(x\). Let's use Equation 1:
\[ -4x - 2(-6) = -12 \]
This becomes:
\[ -4x + 12 = -12 \]
Now, subtract 12 from both sides:
\[ -4x = -12 - 12 \]
\[ -4x = -24 \]
Now, divide both sides by -4:
\[ x = \frac{-24}{-4} \]
\[ x = 6 \]
So, the solution to the system of equations is:
\[ x = 6 \quad \text{and} \quad y = -6 \]
In ordered pair form, the solution is \((6, -6)\).