Question

Solve the following system of equations using the elimination method.

3x−4y=−4 , x+3y=−10

(1 point)
Responses

(−4,−2)
left parenthesis negative 4 comma negative 2 right parenthesis

(−16,2)
left parenthesis negative 16 comma 2 right parenthesis

(−2,−4)
left parenthesis negative 2 comma negative 4 right parenthesis

(−16,−2)

Answer 1

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

1) \( 3x - 4y = -4 \)

2) \( x + 3y = -10 \)

We'll first manipulate the second equation so it can be easily eliminated with the first equation. We can multiply the second equation by 3 to align the \(x\) terms:

1) \( 3x - 4y = -4 \)

2) \( 3(x + 3y) = 3(-10) \) which simplifies to \( 3x + 9y = -30 \)

Now we have the following system:

1) \( 3x - 4y = -4 \)
2) \( 3x + 9y = -30 \)

Next, we will eliminate \(3x\) by subtracting the first equation from the second equation:

\[
(3x + 9y) - (3x - 4y) = -30 - (-4)
\]

This simplifies to:

\[
3x + 9y - 3x + 4y = -30 + 4
\]
\[
13y = -26
\]

Now, divide both sides by 13:

\[
y = -2
\]

Now that we have \(y\), we can substitute it back into one of the original equations to find \(x\). We will use the second equation:

\[
x + 3(-2) = -10
\]
\[
x - 6 = -10
\]
\[
x = -10 + 6
\]
\[
x = -4
\]

So the solution to the system of equations is:

\[
(x, y) = (-4, -2)
\]

The correct response is:

**(−4,−2)**.