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To solve this system of equations by substitution, we start with the two equations given:

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

### Step-by-Step Solution

**Step 1: Substitute the expression for \(y\) from the second equation into the first equation.**

Since \(y = x - 1\), substitute \(x - 1\) for \(y\) in the first equation:

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

**Step 2: Simplify the equation.**

Distribute and combine like terms:

\[
2x - 3x + 3 = -1
\]

\[
-x + 3 = -1
\]

**Step 3: Solve for \(x\).**

Subtract 3 from both sides:

\[
-x = -4
\]

Multiply both sides by -1:

\[
x = 4
\]

**Step 4: Substitute the value of \(x\) back into the equation for \(y\).**

Using the second equation, \(y = x - 1\):

\[
y = 4 - 1 = 3
\]

### Final Solution

The solution to the system of equations is:

\[
x = 4, \; y = 3
\]

Would you like more details or have any questions?

### Related Questions:

1. How do you solve systems of equations using the elimination method?
2. What are the advantages of using substitution versus elimination?
3. How can you check the solution to a system of equations?
4. How can you solve a system of three equations with three variables using substitution?
5. What does it mean if a system of equations has no solution or infinitely many solutions?

**Tip:** Always check your solution by substituting the values back into the original equations to verify they are correct.

Solve each system by substitution: 2x - 3y = -1 and y = x - 1.

Learn how to solve the system of equations 2x - 3y = -1 and y = x - 1 using the substitution method. This step-by-step solution covers algebraic concepts suitable for students in Grades 8-10.

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