Question

Solve the following system of equations using the elimination method.

3x−4y=−4 , x+3y=−10

(1 point)
Responses

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

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

(−4,−2)
left parenthesis negative 4 comma negative 2 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) \(x + 3y = -10\)

First, let's manipulate these equations to eliminate one of the variables. We'll eliminate \(x\) by making the coefficients of \(x\) in both equations the same. We can do this by multiplying the second equation by \(3\):

\[
3(x + 3y) = 3(-10)
\]

This simplifies to:

\[
3x + 9y = -30
\]

Now, we have the modified system:

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

Next, we can eliminate \(x\) by subtracting equation 1 from equation 2:

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

This becomes:

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

Which simplifies to:

\[
13y = -26
\]

Now, we can solve for \(y\):

\[
y = \frac{-26}{13} = -2
\]

Now that we have \(y\), we can substitute it back into one of the original equations to find \(x\). We'll use equation 2:

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

This simplifies to:

\[
x - 6 = -10
\]

Thus, we find:

\[
x = -10 + 6 = -4
\]

So the solution to the system of equations is:

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

The correct response is:

\((-4, -2)\)