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We are asked to solve the system of equations:

\[
y = -x + 3
\]
\[
y = 2x - 3
\]

### Step 1: Set the equations equal to each other.
Since both equations are equal to \(y\), we can set them equal to each other:

\[
-x + 3 = 2x - 3
\]

### Step 2: Solve for \(x\).
First, add \(x\) to both sides:

\[
3 = 3x - 3
\]

Next, add 3 to both sides:

\[
6 = 3x
\]

Now, divide by 3:

\[
x = 2
\]

### Step 3: Substitute \(x = 2\) into one of the original equations.
Substitute into \(y = -x + 3\):

\[
y = -(2) + 3 = -2 + 3 = 1
\]

### Final Answer:
The solution to the system is:

\[
(x, y) = (2, 1)
\]

Would you like more details or have any questions about this solution?

Here are 5 related questions for further practice:
1. What is the graphical interpretation of solving a system of linear equations?
2. How can you solve the same system using the substitution method?
3. How would you solve this system using the elimination method?
4. Can you find a system of equations with no solution? What would that look like?
5. What does it mean when two lines have infinite solutions?

**Tip:** When solving a system of equations, it's helpful to verify the solution by plugging the values of \(x\) and \(y\) into both original equations.

Solve the system of linear equations: y = -x + 3 and y = 2x - 3

Learn how to solve the system of linear equations y = -x + 3 and y = 2x - 3 using the comparison method. This problem covers key algebraic concepts like solving systems of equations and linear functions. Suitable for students in Grades 9-10.

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