To find the points where the system of equations intersect, let's solve the following system:

1. \( x = y - 1 \)
2. \( 3x = 2y \)

### Step 1: Substitute \( x = y - 1 \) into \( 3x = 2y \)
Since \( x \) is already defined as \( y - 1 \) in the first equation, we can substitute this into the second equation:

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

### Step 2: Solve for \( y \)
Expand and simplify the equation:

\[
3y - 3 = 2y
\]

Subtract \( 2y \) from both sides:

\[
y - 3 = 0
\]

\[
y = 3
\]

### Step 3: Find \( x \) using \( y = 3 \)
Substitute \( y = 3 \) back into the first equation:

\[
x = 3 - 1
\]

\[
x = 2
\]

### Solution
The solution is the point where the two lines intersect:
\[
(x, y) = (2, 3)
\]

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

### Related Questions
1. How do you solve a system of equations using the substitution method?
2. What is the graphical interpretation of solving two linear equations?
3. How do you verify if a solution is correct for a system of equations?
4. How can you solve a system of equations using the elimination method?
5. What happens when a system of equations has no solution or infinitely many solutions?

### Tip
Always double-check your substitution when solving equations to avoid mistakes in calculations!

Learn how to solve the system of linear equations x = y - 1 and 3x = 2y using the substitution method. This step-by-step guide demonstrates how to find the point of intersection, covering key algebraic concepts suitable for students in Grades 8-10.

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