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The system of equations given is:

\[
\begin{cases} 
y = -3x + 1 \\
-7x - 3y = -9
\end{cases}
\]

To solve this system, we can substitute \( y = -3x + 1 \) into the second equation.

### Step 1: Substitute \( y = -3x + 1 \) into \( -7x - 3y = -9 \):
\[
-7x - 3(-3x + 1) = -9
\]

Simplify:
\[
-7x + 9x - 3 = -9
\]

\[
2x - 3 = -9
\]

### Step 2: Solve for \( x \):
\[
2x = -6 \quad \Rightarrow \quad x = -3
\]

### Step 3: Solve for \( y \) using \( y = -3x + 1 \):
Substitute \( x = -3 \):
\[
y = -3(-3) + 1 = 9 + 1 = 10
\]

### Final Solution:
\[
x = -3, \, y = 10
\]

Let me know if you need a step-by-step explanation or further clarification! Here are some related questions:

1. How can we verify the solution of a system of equations?
2. What are other methods to solve systems of equations (e.g., elimination)?
3. What are the conditions for a system of equations to have no solution or infinitely many solutions?
4. How does substitution compare to graphing in solving systems of equations?
5. What real-world scenarios involve solving systems of equations?

**Tip:** Always substitute your solution back into the original equations to verify accuracy!

Solve the system of linear equations: y = -3x + 1 and -7x - 3y = -9.

Learn how to solve the system of linear equations y = -3x + 1 and -7x - 3y = -9 using the substitution method. This step-by-step guide explains each step, from substituting one equation into the other to solving for both variables. Ideal for Grades 8-10 students.

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