\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Write the system of linear equations corresponding to the augmented matrix, using variables \(x, y,\) and \(z\).$$ \left[ \begin{array}{ccc|c}-1 & 2 & 2 & -2 \\ 1 & -1 & 5 & 5 \\ \end{array} \right] $$
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