Question

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

2x−4y=−16

Answer 1

To solve the system of equations:

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

We can use either the substitution method or the elimination method. Here, let's use the elimination method.

First, we'll manipulate both equations to make elimination easier. We can simplify Equation 1 by dividing every term by 2:

\[
x + 4y = 4 \quad \text{(Equation 1 simplified)}
\]

Next, we can also simplify Equation 2 by dividing every term by 2:

\[
x - 2y = -8 \quad \text{(Equation 2 simplified)}
\]

Now our system of equations looks like this:

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

Next, we can eliminate \( x \) by subtracting Equation 2 from Equation 1:

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

This simplifies to:

\[
x + 4y - x + 2y = 4 + 8
\]
\[
6y = 12
\]

Now, we solve for \( y \):

\[
y = \frac{12}{6} = 2
\]

Now that we have \( y = 2 \), we can substitute \( y \) back into one of the original equations to solve for \( x \). We'll use Equation 1:

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

Thus, the solution to the system of equations is:

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