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.

Learn how to solve the system of linear equations y = 2 − 3x and y = 2 + x using the substitution method. This problem covers key concepts in solving systems of linear equations and is suitable for students in Grades 9-12.

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