We have the system of linear equations:

1. \( 3x + 2y = 12 \)
2. \( x - y = -12 \)

Let's solve this step by step using the substitution or elimination method.

### Step 1: Solve the second equation for \(x\).
From the second equation:
\[
x - y = -12 \implies x = y - 12
\]

### Step 2: Substitute \(x = y - 12\) into the first equation.
Now, substitute \(x = y - 12\) into the first equation \(3x + 2y = 12\):
\[
3(y - 12) + 2y = 12
\]
Distribute:
\[
3y - 36 + 2y = 12
\]
Combine like terms:
\[
5y - 36 = 12
\]
Add 36 to both sides:
\[
5y = 48
\]
Solve for \(y\):
\[
y = \frac{48}{5}
\]

### Step 3: Substitute \(y = \frac{48}{5}\) back into \(x = y - 12\).
Now that we have \(y = \frac{48}{5}\), substitute this value into the expression for \(x\):
\[
x = \frac{48}{5} - 12
\]
Convert 12 to a fraction with denominator 5:
\[
x = \frac{48}{5} - \frac{60}{5} = \frac{-12}{5}
\]

### Solution:
The solution to the system of equations is:
\[
x = \frac{-12}{5}, \quad y = \frac{48}{5}
\]

Would you like further details or have any questions?

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Here are 5 related questions:

1. How do you solve a system of equations using the elimination method?
2. Can you solve a system of equations graphically?
3. What is the determinant of a system of linear equations?
4. How do you solve systems with more than two equations?
5. What is the significance of consistent and inconsistent systems?

**Tip:** Always double-check solutions by substituting them back into the original equations to verify correctness.

Learn how to solve the system of linear equations 3x + 2y = 12 and x - y = -12 using the substitution method. This step-by-step guide covers key algebraic concepts and methods, making it ideal for students in Grades 8-10.

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