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The given system of linear equations is:

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

To solve this, we can substitute the second equation \( y = x - 1 \) into the first equation:

1. Substitute \( y = x - 1 \) into \( 2x - 3y = -1 \):
   \[
   2x - 3(x - 1) = -1
   \]

2. Simplify the equation:
   \[
   2x - 3x + 3 = -1
   \]

3. Combine like terms:
   \[
   -x + 3 = -1
   \]

4. Solve for \( x \):
   \[
   -x = -1 - 3
   \]
   \[
   -x = -4 \quad \Rightarrow \quad x = 4
   \]

5. Now, substitute \( x = 4 \) into the second equation \( y = x - 1 \):
   \[
   y = 4 - 1 = 3
   \]

So, the solution is \( (x, y) = (4, 3) \).

The correct answer from the given choices is **(4, 3)**.

Would you like more details or have any other questions?

Here are five related questions:
1. How do you solve a system of equations using substitution in general?
2. What is the method of elimination, and how is it different from substitution?
3. How can you check if your solution to a system of linear equations is correct?
4. Can a system of linear equations have no solution or infinitely many solutions?
5. What is the graphical interpretation of solving a system of two linear equations?

**Tip:** Substitution is often useful when one equation is already solved for a variable, as it simplifies the process.

What is the solution to the system of linear equations? 2x - 3y = -1 and y = x - 1

Learn how to solve a system of linear equations, 2x - 3y = -1 and y = x - 1, using the substitution method. Step-by-step guide suitable for Grades 8-10, covering key algebraic concepts and methods.

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