https://file.aiquickdraw.com/mathbot/file/1726860572660orcebmly.jpg

The system of equations you've uploaded is:

\[
\begin{cases}
y = 2x + 2 \\
y = -7x - 1
\end{cases}
\]

We can solve this system using substitution, since both equations are already solved for \(y\).

### Step-by-step solution:
1. Set the right-hand sides of both equations equal to each other since they both equal \(y\):
   \[
   2x + 2 = -7x - 1
   \]

2. Solve for \(x\):
   - First, add \(7x\) to both sides:
     \[
     2x + 7x + 2 = -1
     \]
     \[
     9x + 2 = -1
     \]
   - Then, subtract 2 from both sides:
     \[
     9x = -3
     \]
   - Finally, divide by 9:
     \[
     x = -\frac{1}{3}
     \]

3. Substitute \(x = -\frac{1}{3}\) into either of the original equations to find \(y\). Using \(y = 2x + 2\):
   \[
   y = 2\left(-\frac{1}{3}\right) + 2
   \]
   \[
   y = -\frac{2}{3} + 2
   \]
   \[
   y = -\frac{2}{3} + \frac{6}{3} = \frac{4}{3}
   \]

### Solution:
The solution to the system is:
\[
x = -\frac{1}{3}, \quad y = \frac{4}{3}
\]

Would you like further details on the method used, or have any other questions?

Here are 5 related questions to deepen understanding:
1. How would you solve a system of equations using the elimination method?
2. What would happen if both equations had the same slope?
3. How do you interpret the solution geometrically on a graph?
4. Can systems of equations have more than one solution? Why or why not?
5. How do you solve a system of equations with more than two variables?

**Tip**: When solving systems of equations, always check the solution by substituting back into both original equations to ensure consistency.

Solve the system of equations: y = 2x + 2 and y = -7x - 1

Learn how to solve a system of linear equations using the substitution method. This example solves y = 2x + 2 and y = -7x - 1 step-by-step, suitable for students in Grades 8-10.

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