https://file.aiquickdraw.com/mathbot/file/1729549440624flj8e8cr.jpg

The system of linear equations given in the image is:

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

### Step 1: Solve the second equation for \(y\).
The second equation is:
\[
y - x = -2
\]
Add \(x\) to both sides:
\[
y = x - 2
\]

### Step 2: Substitute \(y = x - 2\) into the first equation.
Substitute this into the first equation:
\[
x - 2(x - 2) = 1
\]
Simplify:
\[
x - 2x + 4 = 1
\]
\[
-x + 4 = 1
\]
Subtract 4 from both sides:
\[
-x = -3
\]
Multiply both sides by \(-1\):
\[
x = 3
\]

### Step 3: Substitute \(x = 3\) back into the equation for \(y\).
Now substitute \(x = 3\) into the equation \(y = x - 2\):
\[
y = 3 - 2 = 1
\]

### Solution:
The solution to the system of equations is:
\[
x = 3, \quad y = 1
\]

Would you like more details on how to solve such systems, or do you have any questions?

Here are 5 related questions you might explore:
1. How do you solve a system of equations by substitution?
2. What is the elimination method for solving systems of equations?
3. How can you represent a system of linear equations graphically?
4. Can systems of equations have no solution or infinitely many solutions?
5. How does solving systems of equations apply in real-world problems?

**Tip**: When solving systems of equations, always simplify and substitute carefully to avoid errors.

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

Learn how to solve the system of linear equations x - 2y = 1 and y - x = -2 using substitution and simplification methods. Detailed steps guide you through solving for x and y, making it suitable for students in Grades 8-10.

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