Question

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

2x−4y=−16
(1 point)
(
,
)
Remaining Attempts

Answer 1

To solve the system of equations:

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

Let's simplify each equation first.

**From Equation 1:**
\[
2x + 8y = 8
\]
Dividing the entire equation by 2:
\[
x + 4y = 4 \quad (1)
\]

**From Equation 2:**
\[
2x - 4y = -16
\]
Dividing the entire equation by 2:
\[
x - 2y = -8 \quad (2)
\]

Now we can solve these two simplified equations:
1. \( x + 4y = 4 \)
2. \( x - 2y = -8 \)

Next, we can substitute \( x \) from Equation (2) into Equation (1).

From Equation (2), we can express \( x \) as:
\[
x = -8 + 2y
\]

Now substitute this into Equation (1):
\[
(-8 + 2y) + 4y = 4
\]

Combine like terms:
\[
-8 + 6y = 4
\]
Add 8 to both sides:
\[
6y = 12
\]
Divide by 6:
\[
y = 2
\]

Now substitute \( y = 2 \) back into the expression for \( x \):
\[
x = -8 + 2(2)
\]
\[
x = -8 + 4
\]
\[
x = -4
\]

So the solution to the system of equations is:
\[
(x, y) = (-4, 2)
\]

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