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.