https://file.aiquickdraw.com/mathbot/file/17288695071034ndpxab4.jpg

The system of equations to solve is:

\[
\begin{cases}
-x + y = -3 \\
4x - 3y = 12
\end{cases}
\]

We'll use the substitution method to solve this.

### Step 1: Solve one of the equations for one variable
From the first equation, we can solve for \( y \):

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

### Step 2: Substitute the expression for \( y \) into the second equation
Substitute \( y = x - 3 \) into the second equation:

\[
4x - 3(x - 3) = 12
\]

### Step 3: Simplify and solve for \( x \)
Expand the equation:

\[
4x - 3x + 9 = 12
\]

\[
x + 9 = 12
\]

Subtract 9 from both sides:

\[
x = 3
\]

### Step 4: Substitute \( x = 3 \) into the expression for \( y \)
Now substitute \( x = 3 \) into \( y = x - 3 \):

\[
y = 3 - 3 = 0
\]

### Final Answer:
\[
x = 3, \quad y = 0
\]

Let me know if you'd like further clarification!

Here are some follow-up questions:

1. How can the substitution method be applied to nonlinear systems?
2. How does the substitution method compare to the elimination method?
3. Can the substitution method be used for systems with more than two variables?
4. What are the advantages of solving systems graphically versus algebraically?
5. What does the solution \( (x, y) = (3, 0) \) represent geometrically?

**Tip:** When solving systems, always check your solution by substituting both values back into the original equations.

Use the substitution method to solve the system of equations: -x + y = -3 and 4x - 3y = 12.

Learn how to solve the system of linear equations -x + y = -3 and 4x - 3y = 12 using the substitution method. This step-by-step solution covers key algebraic concepts and is suitable for students in Grades 8-10.

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