Determine the values of $x, y$, and $z$ for the following set of linear algebraic equations: [begin{aligned}&

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Determine the values of $x, y$, and $z$ for the following set of linear algebraic equations:

\[\begin{aligned}& 2 x-y=10 \\& -x+2 y-z=0 \\& -y+z=-50\end{aligned}\]

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