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Use Cramer's Rule to Solve (If Possible) the System of Equations

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Use Cramer's Rule to solve (if possible) the system of equations.
{5x4y+z=12x+2y2z=123x+y+z=2\left\{ \begin{array} { r } 5 x - 4 y + z = - 12 \\- x + 2 y - 2 z = 12 \\3 x + y + z = - 2\end{array} \right.


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