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The system of equations given is:

\[
\begin{aligned}
-2x + y &= 9 \\
5x + y &= -12
\end{aligned}
\]

### Step-by-Step Solution:
1. **First equation**: \(-2x + y = 9\)
2. **Second equation**: \(5x + y = -12\)

We will solve this system using the method of elimination or substitution.

#### Substitution or Elimination Method:
1. From the first equation, we can isolate \(y\):
   \[
   y = 9 + 2x
   \]
2. Substitute \(y = 9 + 2x\) into the second equation:
   \[
   5x + (9 + 2x) = -12
   \]
   Simplifying:
   \[
   5x + 2x + 9 = -12
   \]
   \[
   7x + 9 = -12
   \]
   Solving for \(x\):
   \[
   7x = -12 - 9
   \]
   \[
   7x = -21
   \]
   \[
   x = -3
   \]

3. Now, substitute \(x = -3\) back into the expression for \(y\):
   \[
   y = 9 + 2(-3)
   \]
   \[
   y = 9 - 6 = 3
   \]

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

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve systems of equations using the substitution method?
2. Can we use the elimination method to solve the same system of equations?
3. What are other methods for solving systems of linear equations?
4. How can you check if a solution to a system of equations is correct?
5. What is the graphical interpretation of the solution to a system of linear equations?

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

Solve the following system of equations:
-2x + y = 9
5x + y = -12

Learn how to solve the system of equations -2x + y = 9 and 5x + y = -12 using the substitution method. This solution is suitable for students in Grades 8-10 and includes a step-by-step approach for finding the values of x and y.

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