Question

The system of equations is graphed on the coordinate plane.

y=−x−2y=3x+2

Enter the coordinates of the solution to the system of equations in the boxes.

Answer 1

To find the solution to the system of equations given by:

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

we can set them equal to each other since they both equal \( y \):

\[
-x - 2 = 3x + 2
\]

Now, let's solve for \( x \):

1. Add \( x \) to both sides:
\[
-2 = 4x + 2
\]

2. Subtract \( 2 \) from both sides:
\[
-4 = 4x
\]

3. Divide by \( 4 \):
\[
x = -1
\]

Now that we have \( x = -1 \), we can substitute it back into either equation to find \( y \). We'll use the first equation:

\[
y = -(-1) - 2 = 1 - 2 = -1
\]

Thus, the coordinates of the solution to the system of equations are:

\[
(x, y) = (-1, -1)
\]

Therefore, the answer is:
\[
\text{Coordinates: } (-1, -1)
\]