We have the following system of equations:

\[
1) \ 2x - y = -12 
\]
\[
2) \ -2x + y = 12
\]

To solve this system, we can use the **elimination method**. 

### Step 1: Add the two equations together.

\[
(2x - y) + (-2x + y) = -12 + 12
\]

Simplifying:

\[
0 = 0
\]

This equation indicates that the two equations are **dependent**, meaning they represent the same line. So, there are **infinitely many solutions**. 

### Step 2: Write the solution in parametric form.
From the first equation, solve for \(y\) in terms of \(x\):

\[
y = 2x + 12
\]

Thus, the general solution for the system is:

\[
\boxed{(x, y) = (x, 2x + 12)} \quad \text{where} \ x \ \text{can be any real number.}
\]

Let me know if you'd like further details or have any questions!

Here are 5 related questions to consider:
1. How do you interpret the parametric solution geometrically?
2. What would happen if the system had no solution?
3. How can you verify that two equations are dependent?
4. What is the difference between a dependent and independent system of equations?
5. How can you solve this system using substitution?

**Tip:** Always check your solution by substituting it back into the original equations.

Learn how to solve the system of linear equations 2x − y = −12 and −2x + y = 12 using the elimination method. Discover how dependent systems have infinitely many solutions and how to express the solution in parametric form. This guide is ideal for high school students in Grades 9-12.

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