To graph the system of equations:

1. **Equation 1**: \( x = y - 1 \) 
   - Solve for \( y \) to make graphing easier: 
     \[
     y = x + 1
     \]
   This is a straight line with slope \(1\) and y-intercept \(1\).

2. **Equation 2**: \( 3x = 2y \)
   - Solve for \( y \): 
     \[
     y = \frac{3}{2}x
     \]
   This is a straight line with slope \( \frac{3}{2} \) and y-intercept \(0\).

### Graphing these lines:
- The first line, \( y = x + 1 \), has a slope of \(1\) and crosses the y-axis at \( (0, 1) \).
- The second line, \( y = \frac{3}{2}x \), has a slope of \( \frac{3}{2} \) and crosses the y-axis at \( (0, 0) \).

The intersection of these two lines can be found by solving the system algebraically or by graphing them. The solution to the system represents the point where the two lines meet.

Would you like me to provide the exact solution for the intersection point or more details on the graph?

Here are 5 related questions:
1. What is the solution to this system of equations?
2. How do you determine the slope of a line from its equation?
3. Can systems of equations have no solution? Why or why not?
4. How can we identify parallel lines from their equations?
5. What are the different methods to solve systems of equations (besides graphing)?

**Tip**: When graphing linear equations, always start by identifying the slope and y-intercept for easier plotting.

Learn how to graph the system of linear equations x = y - 1 and 3x = 2y. This solution covers key algebraic concepts, including solving for y, determining slopes, and understanding y-intercepts. Suitable for students in Grades 8-10.

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