Question

Solving with Elimination Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
2 of 52 of 5 Items


Question
Solve the system of equations.
2x+8y=8

2x−4y=−16
(1 point)
(
,
)

Answer 1

To solve the system of equations using the elimination method, we have the following equations:

1) \( 2x + 8y = 8 \)
2) \( 2x - 4y = -16 \)

First, let's align the equations for clarity:

\[
\begin{align*}
(1) & \quad 2x + 8y = 8 \\
(2) & \quad 2x - 4y = -16 \\
\end{align*}
\]

Next, we can eliminate \(x\) by subtracting one equation from the other. To do this, we can first multiply equation (2) by -1 so that we can eliminate \(2x\):

\[
-1 \cdot (2x - 4y) = -1 \cdot (-16) \implies -2x + 4y = 16
\]

Now we can rewrite our system:

1) \( 2x + 8y = 8 \)
2) \( -2x + 4y = 16 \)

Next, we can add the two equations together:

\[
(2x + 8y) + (-2x + 4y) = 8 + 16
\]

This simplifies to:

\[
0x + 12y = 24
\]

Thus, we can solve for \(y\):

\[
12y = 24 \quad \implies \quad y = \frac{24}{12} = 2
\]

Now that we have the value for \(y\), let's substitute \(y = 2\) back into one of the original equations to find \(x\). We'll use equation (1):

\[
2x + 8(2) = 8
\]

This simplifies to:

\[
2x + 16 = 8
\]

Now, we isolate \(2x\):

\[
2x = 8 - 16 \quad \implies \quad 2x = -8 \quad \implies \quad x = -4
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-4, 2)
\]

The final answer is:

\[
\boxed{(-4, 2)}
\]