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This exercise has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer's rule. Use each method at least once when solving the systems. Include solutions with nonreal complex number components. For systems with infinitely many solutions, write the solution set using an arbitrary variable.

$\begin{aligned} & -5 x+2 y+z=5 \\ & -3 x-2 y-z=3 \\ & -x+6 y=1 \end{aligned}$

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1 of 5To solve a system of linear equations with three unknowns, use the elimination method and substitution method.

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