https://file.aiquickdraw.com/mathbot/file/1726311522543j83c04nt.jpg

https://file.aiquickdraw.com/mathbot/file/1726311537619mnaemfw3.jpg

I can see the system of equations from the uploaded image:

\[
-x + y = -2 \quad \text{(1)}
\]
\[
3x + y = 2 \quad \text{(2)}
\]

### Step 1: Solve the first equation for \( y \)

From equation (1):
\[
-x + y = -2
\]
Add \( x \) to both sides:
\[
y = x - 2
\]

### Step 2: Substitute into the second equation

Now, substitute \( y = x - 2 \) into the second equation \( 3x + y = 2 \):
\[
3x + (x - 2) = 2
\]
Simplify:
\[
3x + x - 2 = 2
\]
\[
4x - 2 = 2
\]
Add 2 to both sides:
\[
4x = 4
\]
Divide by 4:
\[
x = 1
\]

### Step 3: Find \( y \)

Now that \( x = 1 \), substitute it back into \( y = x - 2 \):
\[
y = 1 - 2 = -1
\]

### Solution:
The solution to the system of equations is:
\[
(x, y) = (1, -1)
\]

Would you like any further details or clarifications?

Here are 5 related questions to consider:
1. How can we verify the solution of a system of equations?
2. What are the different methods to solve a system of linear equations?
3. Can all systems of linear equations have unique solutions?
4. How does graphing help in solving a system of equations?
5. What does it mean when a system of equations has no solution or infinitely many solutions?

**Tip**: Substitution is often a simpler method when one equation is already solved for a variable.

-x + y = -2, 3x + y = 2. First equation solved in the form y = ?. What is the solution (x, y)?

Learn how to solve the system of linear equations: -x + y = -2 and 3x + y = 2. This problem is solved using the substitution method, and it's suitable for students in grades 8-10.

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