Question

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

2x−4y=−16
(1 point)
(
,
)

Answer 1

To solve the system of equations, we have:

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

We can solve this system using either substitution or elimination. Here, let's use elimination.

First, we can simplify both equations if needed.

Starting with the first equation:
1. \( 2x + 8y = 8 \) can be divided by 2:
\[
x + 4y = 4
\]

Now the first equation is:
\[
x + 4y = 4 \tag{1}
\]

Now simplify the second equation:
2. \( 2x - 4y = -16 \) can also be divided by 2:
\[
x - 2y = -8
\]

Now the second equation is:
\[
x - 2y = -8 \tag{2}
\]

Now we will subtract equation (1) from equation (2) to eliminate \(x\):
\[
(x - 2y) - (x + 4y) = -8 - 4
\]
This simplifies to:
\[
-2y - 4y = -12
\]
Combine like terms:
\[
-6y = -12
\]

Now, divide by -6:
\[
y = 2
\]

Now that we have the value of \(y\), we can substitute it back into one of the original equations to find \(x\). We'll use equation (1):
\[
x + 4(2) = 4
\]
This simplifies to:
\[
x + 8 = 4
\]
Subtracting 8 from both sides gives:
\[
x = 4 - 8
\]
\[
x = -4
\]

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

So the answer is:
\[
(-4, 2)
\]