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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.

Solve the following system of equations: -6x + 3y - z = 5, 3x - y + 5z = -10, -x + 2y + 3z = -1.

Learn how to solve the system of linear equations: -6x + 3y - z = 5, 3x - y + 5z = -10, and -x + 2y + 3z = -1. This problem uses techniques like substitution and elimination. Suitable for high school students.

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