Question

Solve the following system of equations using the elimination method.

3x−4y=−4
, x+3y=−10

(1 point)
Responses

(−16,−2)
left parenthesis negative 16 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

(−4,−2)

Answer 1

To solve the system of equations using the elimination method, we start with the given equations:

1) \( 3x - 4y = -4 \)
2) \( x + 3y = -10 \)

We can eliminate one of the variables by multiplying one or both of the equations. Let's eliminate \( x \).

First, we'll multiply the second equation by 3:

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

which simplifies to:

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

Now we have the transformed system of equations:

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

Next, we'll subtract equation (1) from equation (3) to eliminate \( x \):

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

This simplifies to:

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

Now, solve for \( y \):

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

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

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

Thus, the solution to the system of equations is:

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

The correct response is:

\((−4,−2)\)