The solution to the system of equations is:

$x = -5, \quad y = -5, \quad z = 3$

Would you like further details on how this solution was obtained?

Here are 5 related questions for deeper exploration:

1. How do you solve systems of linear equations using substitution?
2. What is the method of elimination, and how does it apply here?
3. Can matrix methods like Gaussian elimination be used for this system?
4. How do we verify solutions to systems of linear equations?
5. What are some real-world applications of solving such systems?

Tip: When solving systems of equations, always double-check your algebraic manipulations to avoid small mistakes that can lead to incorrect solutions.