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The problem asks you to solve the following system of linear equations by graphing:

\[
\begin{aligned}
y &= -1x - 1 \\
y &= 2x - 7
\end{aligned}
\]

We can solve this system by graphing the two equations and finding the intersection point, as that represents the solution where both equations are satisfied.

### Steps to graph the equations:

1. **First equation: \( y = -x - 1 \)**
   - Slope: \( -1 \) (which means for every step right, go down 1 unit)
   - Y-intercept: \( -1 \) (the point where the line crosses the y-axis)
   - Plot the y-intercept (0, -1) and use the slope to find additional points.

2. **Second equation: \( y = 2x - 7 \)**
   - Slope: \( 2 \) (for every step right, go up 2 units)
   - Y-intercept: \( -7 \)
   - Plot the y-intercept (0, -7) and use the slope to find additional points.

### Finding the intersection:
When graphing both lines, they intersect at a single point. This point is the solution to the system of equations. Alternatively, solving algebraically by setting the two equations equal to each other:

\[
-x - 1 = 2x - 7
\]

Solving for \( x \):
\[
-x - 1 = 2x - 7
\]
\[
-1 - (-7) = 2x + x \quad \Rightarrow \quad 6 = 3x
\]
\[
x = 2
\]

Substitute \( x = 2 \) into one of the original equations to find \( y \):
\[
y = 2(2) - 7 = 4 - 7 = -3
\]

Thus, the solution is:
\[
(x, y) = (2, -3)
\]

Would you like further details or have any questions?

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Here are 5 related questions you could explore:
1. How can you verify the solution to a system of equations?
2. What are other methods to solve systems of equations besides graphing?
3. What is the geometric interpretation of the solution to a system of equations?
4. How would you solve the system if both lines were parallel?
5. How can a system of equations have no solution or infinitely many solutions?

**Tip:** Always double-check your graph by plugging the solution back into the original equations to ensure it satisfies both.

Solve the system of linear equations: y = -1x - 1 and y = 2x - 7 using a graphing utility.

Learn how to solve the system of linear equations y = -1x - 1 and y = 2x - 7 by graphing. This problem covers key algebraic concepts, including finding the intersection of lines, and provides a detailed solution suitable for students in Grades 8-10.

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