Question

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

2x−6y=8
(1 point)
Responses

(−2, 3)
(−2, 3)
- no response given

(−5,−3)

Answer 1

To solve the system of equations:

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

Let's solve these equations step by step.

First, we can simplify Equation 1:

1. Divide the entire equation by 4:
\[
2x - y = -7 \quad \text{(Equation 3)}
\]

Now we have:
- Equation 3: \( 2x - y = -7 \)
- Equation 2: \( 2x - 6y = 8 \)

Next, we can use Equation 3 to solve for \( y \) in terms of \( x \):
\[
y = 2x + 7 \quad \text{(Equation 4)}
\]

Now, substitute Equation 4 into Equation 2:
\[
2x - 6(2x + 7) = 8
\]
Distributing -6:
\[
2x - 12x - 42 = 8
\]
Combining like terms:
\[
-10x - 42 = 8
\]
Adding 42 to both sides:
\[
-10x = 50
\]
Dividing both sides by -10:
\[
x = -5
\]

Now, substitute \( x = -5 \) back into Equation 4 to find \( y \):
\[
y = 2(-5) + 7
\]
\[
y = -10 + 7
\]
\[
y = -3
\]

So, the solution to the system of equations is:
\[
(x, y) = (-5, -3)
\]

Therefore, the correct response is:
\[
(-5, -3)
\]