Question

Solve the system of linear equations using the elimination method. Write your answer as a coordinate on the xy
-coordinate plane.

y+3x=−2


2y−3x=14


(1 point)
Responses

(-2, 4)
(-2, 4)

(-6, 16)
(-6, 16)

(4, -2)
(4, -2)

(6, 16)
(6, 16)

Answer 1

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

1. \( y + 3x = -2 \)
2. \( 2y - 3x = 14 \)

First, let's manipulate these equations to eliminate one of the variables.

We can add the two equations to eliminate \( x \). To do this, we can first rearrange the first equation to isolate \( y \):

1. \( y = -2 - 3x \)

Now, substitute this expression for \( y \) into the second equation:

\[
2(-2 - 3x) - 3x = 14
\]

Now, distribute and simplify:

\[
-4 - 6x - 3x = 14
\]
\[
-4 - 9x = 14
\]

Now, add 4 to both sides:

\[
-9x = 18
\]

Divide by -9:

\[
x = -2
\]

Next, substitute \( x = -2 \) back into the first equation to find \( y \):

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

Thus, the solution to the system of equations is

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

As a coordinate on the xy-coordinate plane, the solution is \((-2, 4)\).

Therefore, the correct response is:

**(-2, 4)**