The solution to the system of equations is:

$x = 1, \quad y = 3, \quad z = -2$

Would you like any further details or clarifications on how this solution was derived?

Here are some related questions to explore further:

1. How do you solve a system of linear equations using substitution?
2. What are the methods for solving a system of equations: substitution, elimination, or matrices?
3. How can we check the consistency of a system of equations?
4. What are the geometric interpretations of solving three-variable systems?
5. How does Cramer's Rule work for solving systems of equations?

Tip: For large systems of equations, using matrices or computer tools like Python (SymPy) or MATLAB can be very helpful for quickly finding solutions.