https://file.aiquickdraw.com/mathbot/file/173324788690727zritx1.jpg

The system of linear equations provided is:

\[
\begin{cases}
4x + 2y = -2 \\
-4x - y = 7
\end{cases}
\]

### Solving this system step-by-step:

1. **Simplify the second equation for \(y\):**
   \[
   -4x - y = 7 \quad \Rightarrow \quad y = -4x - 7
   \]

2. **Substitute \(y = -4x - 7\) into the first equation:**
   \[
   4x + 2(-4x - 7) = -2
   \]
   Simplify:
   \[
   4x - 8x - 14 = -2
   \]
   \[
   -4x - 14 = -2
   \]
   \[
   -4x = 12 \quad \Rightarrow \quad x = -3
   \]

3. **Substitute \(x = -3\) into \(y = -4x - 7\):**
   \[
   y = -4(-3) - 7
   \]
   \[
   y = 12 - 7 = 5
   \]

### Final Solution:
\[
x = -3, \, y = 5
\]

Would you like additional explanations or details about this process?

---

### Expanding Questions:
1. What is the geometric interpretation of solving a system of equations?
2. How can substitution and elimination methods be compared in terms of efficiency?
3. What role does checking the solution play in solving systems of equations?
4. How can this system of equations be solved graphically?
5. How would the solution process change if we were solving this system for a parameterized value?

**Tip:** Always verify your solution by substituting the values of \(x\) and \(y\) back into the original equations.

Solve the system of linear equations: {4x + 2y = -2, -4x - y = 7}.

Discover how to solve the system of linear equations 4x + 2y = -2 and -4x - y = 7 step-by-step using the substitution method. Ideal for students in Grades 8-10, this tutorial covers key algebraic concepts and verification steps.

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