https://file.aiquickdraw.com/mathbot/file/1726771091421i79028yq.jpg

The system of equations provided in the image is:

\[
\begin{cases}
x + y = 5 \\
x - 2y = -1
\end{cases}
\]

Let's solve this system of linear equations using substitution or elimination. I will use the substitution method here.

1. From the first equation, solve for \( x \):
   \[
   x = 5 - y
   \]

2. Substitute \( x = 5 - y \) into the second equation:
   \[
   (5 - y) - 2y = -1
   \]

3. Simplify the equation:
   \[
   5 - y - 2y = -1 \quad \Rightarrow \quad 5 - 3y = -1
   \]

4. Solve for \( y \):
   \[
   -3y = -1 - 5 \quad \Rightarrow \quad -3y = -6 \quad \Rightarrow \quad y = 2
   \]

5. Substitute \( y = 2 \) back into the equation \( x = 5 - y \):
   \[
   x = 5 - 2 = 3
   \]

Thus, the solution to the system is \( x = 3 \) and \( y = 2 \).

Would you like more details, or do you have any questions?

Here are five related questions to expand on this topic:
1. How can you solve this system using the elimination method?
2. What happens if we graph these two equations on the coordinate plane?
3. Can you solve a similar system with three variables?
4. What is the general approach for solving nonlinear systems?
5. How do you check the solution of a system of equations?

**Tip:** When solving systems of equations, always double-check your solution by substituting the values back into both original equations.

Solve the system of equations: x + y = 5 and x - 2y = -1.

Learn how to solve the system of linear equations x + y = 5 and x - 2y = -1 using the substitution method. This solution is ideal for students in Grades 7-9, covering key algebra concepts such as substitution and elimination methods.

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