Question

Solve the system of equations.
8x−4y=−28

2x−6y=8
(1 point)
Responses

(−2, 3)
left parenthesis negative 2 comma 3 right parenthesis

(−4,−1)
left parenthesis negative 4 comma negative 1 right parenthesis

(7, 1)
left parenthesis 7 comma 1 right parenthesis

(−5,−3)

Answer 1

To solve the system of equations

1. \( 8x - 4y = -28 \)
2. \( 2x - 6y = 8 \)

we can use the substitution or elimination method. Let's use the elimination method.

First, simplify the equations if possible.

For the first equation, divide all terms by 4:

\[
2x - y = -7 \quad \text{(Equation 1)}
\]

For the second equation, leave it as is or divide it by 2:

\[
x - 3y = 4 \quad \text{(Equation 2)}
\]

Now, we have the simplified system:

1. \( 2x - y = -7 \)
2. \( x - 3y = 4 \)

Next, we can express \( y \) in terms of \( x \) from Equation 1:

\[
y = 2x + 7
\]

Now substitute this expression for \( y \) into Equation 2:

\[
x - 3(2x + 7) = 4
\]

This simplifies to:

\[
x - 6x - 21 = 4
\]
\[
-5x - 21 = 4
\]
\[
-5x = 4 + 21
\]
\[
-5x = 25
\]
\[
x = -5
\]

Now that we have \( x \), substitute back to find \( y \):

\[
y = 2(-5) + 7
\]
\[
y = -10 + 7
\]
\[
y = -3
\]

Thus, the solution is \( (x, y) = (-5, -3) \).

The solution to the system of equations is:

\[
\boxed{(-5, -3)}
\]

So the correct response from the options provided is \( \text{(−5,−3)} \).