The solution to the system of equations using Cramer's rule is:

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

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Here are 5 related questions to expand on this topic:

1. How is Cramer's rule derived for a 3x3 system?
2. What are the limitations of using Cramer's rule in solving systems of equations?
3. Can Cramer's rule be used for a system with infinite solutions?
4. How can determinants help in understanding the properties of linear systems?
5. What happens if the determinant of the coefficient matrix is zero?

Tip: Always check the determinant of the coefficient matrix before applying Cramer's rule—if it's zero, the system has no unique solution.