Question

Here's the question and answer options from the image:

Question:
"Solve the following system of equations using the elimination method.
7x+4y=−4
5x+8y=28
(1 point)"

Answer Options:

(−4,−8)
(−4,6)
(4,−8)
(6,−4)

Answer 1

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

1. \( 7x + 4y = -4 \) (Equation 1)
2. \( 5x + 8y = 28 \) (Equation 2)

First, we can multiply Equation 1 so that the coefficients of \(y\) in both equations will match. We can multiply Equation 1 by \(2\):

\[
2(7x + 4y) = 2(-4)
\]

This gives us:

\[
14x + 8y = -8 \quad (Equation 3)
\]

Now we have:

1. \( 14x + 8y = -8 \) (Equation 3)
2. \( 5x + 8y = 28 \) (Equation 2)

Next, we can eliminate \(y\) by subtracting Equation 2 from Equation 3:

\[
(14x + 8y) - (5x + 8y) = -8 - 28
\]

This simplifies to:

\[
9x = -36
\]

Now, solve for \(x\):

\[
x = -4
\]

Now, substitute \(x = -4\) back into one of the original equations to find \(y\). Let's use Equation 1:

\[
7(-4) + 4y = -4
\]

This simplifies to:

\[
-28 + 4y = -4
\]

Now, solve for \(y\):

\[
4y = -4 + 28
\]
\[
4y = 24
\]
\[
y = 6
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-4, 6)
\]

The correct answer from the options provided is:

**(−4, 6)**