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We are given the system of linear equations:

\[
\begin{aligned}
- x + 4y &= -12 \quad \text{(1)} \\
3x - 6y &= 6 \quad \text{(2)}
\end{aligned}
\]

Let's solve this system by substitution.

### Step 1: Solve for \( x \) in terms of \( y \) from equation (1).
From equation (1):
\[
- x + 4y = -12
\]
Solve for \( x \):
\[
x = 4y + 12
\]

### Step 2: Substitute \( x = 4y + 12 \) into equation (2).
Now, replace \( x \) in equation (2) with \( 4y + 12 \):
\[
3(4y + 12) - 6y = 6
\]
Expand the equation:
\[
12y + 36 - 6y = 6
\]
Simplify:
\[
6y + 36 = 6
\]
Subtract 36 from both sides:
\[
6y = -30
\]
Solve for \( y \):
\[
y = -5
\]

### Step 3: Substitute

-x + 4y = -12, 3x - 6y = 6. Solve by substitution.

Learn how to solve the system of linear equations -x + 4y = -12 and 3x - 6y = 6 using the substitution method. This step-by-step solution involves solving for x in terms of y and substituting it into the second equation. Suitable for Grades 8-10.

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