Question

8x−4y=−28 2x−6y=8 (1 point) Responses (−4,−1) left parenthesis negative 4 comma negative 1 right parenthesis (−2, 3) left parenthesis negative 2 comma 3 right parenthesis (−5,−3) left parenthesis negative 5 comma negative 3 right parenthesis (7, 1)

Answer 1

To solve the system of equations:

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

We'll solve this system using the substitution or elimination method. Let's start with the elimination method.

First, let's simplify Equation 1 by dividing every term by 4:

\[
2x - y = -7 \quad (Equation 3)
\]

Next, we'll work with Equation 2, which is already in a simpler form.

Now we have:

1. \( 2x - y = -7 \) (Equation 3)
2. \( 2x - 6y = 8 \) (Equation 2)

Next, we can use (2x - y = -7) to express \( y \) in terms of \( x \):

From Equation 3:

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

Now, we can substitute Equation 4 back into Equation 2:

\[
2x - 6(2x + 7) = 8
\]

Distributing the -6:

\[
2x - 12x - 42 = 8
\]

Combine like terms:

\[
-10x - 42 = 8
\]

Add 42 to both sides:

\[
-10x = 50
\]

Now, divide by -10:

\[
x = -5
\]

Now substitute \( x = -5 \) back into Equation 4 to find \( y \):

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

So the solution to the system of equations is:

\[
(x, y) = (-5, -3)
\]

Thus, the correct response is:

\((-5, -3)\)