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

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

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

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

(6, 16)

Answer 1

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

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

Let's arrange the equations for elimination:

From Equation 1, we can express \( y \) in terms of \( x \):
\[
y = -2 - 3x
\]

Next, we'll substitute this expression for \( y \) into Equation 2 to eliminate \( y \):

Substituting into Equation 2:
\[
2(-2 - 3x) - 3x = 14
\]

Distributing the 2:
\[
-4 - 6x - 3x = 14
\]

Combining like terms:
\[
-4 - 9x = 14
\]

Adding 4 to both sides:
\[
-9x = 18
\]

Dividing by -9:
\[
x = -2
\]

Now that we have \( x \), we can substitute it back into the expression for \( y \):
\[
y = -2 - 3(-2)
\]
\[
y = -2 + 6
\]
\[
y = 4
\]

So the solution to the system of equations is:
\[
(x, y) = (-2, 4)
\]

The coordinate on the xy-coordinate plane is:
\[
\boxed{(-2, 4)}
\]