To solve the system of linear equations:

$y = 2 - 3x$ $y = 2 + x$

we can use the substitution or elimination method. Here, we will use the substitution method since both equations are already solved for $y$.

1. Set the right-hand sides of the equations equal to each other:

$2 - 3x = 2 + x$

2. Solve for $x$:

$2 - 3x = 2 + x$ $2 - 2 = 3x + x$ $0 = 4x$ $x = 0$

3. Substitute $x = 0$ back into one of the original equations to find $y$:

Using $y = 2 + x$:

$y = 2 + 0$ $y = 2$

Thus, the solution to the system of equations is:

$x = 0$ $y = 2$

Would you like more details or have any questions about this solution? Here are 5 additional questions you might find interesting:

1. How do you solve a system of equations using the elimination method?
2. What are the different methods to solve systems of linear equations?
3. How can you determine if a system of equations has no solution or infinitely many solutions?
4. What is the graphical interpretation of solving a system of linear equations?
5. Can you solve a system of nonlinear equations?

Tip: When solving systems of linear equations, always check if one method might be simpler than others based on how the equations are presented.