Determine the values of $x, y$, and $mathrm{z}$ for the following set of linear algebraic equations: [begin{aligned}x_{2}-3

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

\[\begin{aligned}x_{2}-3 x_{3} & =-7 \\2 x_{1}+3 x_{2}-x_{3} & =9 \\4 x_{1}+5 x_{2}-2 x_{3} & =15\end{aligned}\]

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