Question

The system of equations is graphed on the coordinate plane.

y=x−1y=−2x−4

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

(
, ​
)

A graph with a blue line passing through coordinates (-2, 0), (-1, -2) and (0, -4) and a red line passing through coordinates (-1, -2), (0, -1) and (1, 0).

Answer 1

To find the solution to the system of equations \( y = x - 1 \) and \( y = -2x - 4 \), we need to determine where the two lines intersect.

1. **Set the equations equal to each other**:

\[
x - 1 = -2x - 4
\]

2. **Solve for x**:

\[
x + 2x = -4 + 1
\]
\[
3x = -3
\]
\[
x = -1
\]

3. **Substitute \( x = -1 \) back into one of the original equations to find y**. We'll use \( y = x - 1 \):

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

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

\[
(-1, -2)
\]

So, the answer is:

\[
\left(-1, -2\right)
\]