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We are tasked with solving the system of three linear equations:

\[
\begin{aligned}
1. \quad & x + y + z = -5 \\
2. \quad & -2x - y + z = -1 \\
3. \quad & x - 2y - z = 0
\end{aligned}
\]

Let's solve this system step by step using substitution or elimination. I'll start by reducing the system and finding the values for \(x\), \(y\), and \(z\).

First, I'll subtract equations from one another to eliminate one variable and solve for the remaining ones. Let's calculate.

The solution to the system of equations is:

\[
x = -2, \quad y = 1, \quad z = -4
\]

Would you like further details or explanations on the method used? 

Here are 5 related questions to deepen your understanding:
1. How can substitution be applied to solve a system of three equations?
2. What is the elimination method, and how does it simplify solving systems of equations?
3. How can you check the solution of a system of equations?
4. What role does matrix algebra play in solving larger systems of equations?
5. How do systems of equations apply to real-world problems, such as in physics or economics?

**Tip:** Always verify your solution by substituting the values back into the original equations!

Solve the system of equations:
1. x + y + z = -5
2. -2x - y + z = -1
3. x - 2y - z = 0

This page provides a detailed solution to a system of linear equations: x + y + z = -5, -2x - y + z = -1, and x - 2y - z = 0. The solution involves using substitution and elimination methods, suitable for students in Grades 9-12.

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