\left\{ \begin{array} { c } { - 2 k z + 4 x + y = - 2 k ^ { 2 } } \\ { - 2 k y + 4 x - z = - k } \\ { ( 8 k + 12 ) x + ( - 2 k - 3 ) y + ( - 16 k + 4 ) z = - 2 } \end{array} \right.
Solve for x, y, z
\left\{\begin{matrix}x=\frac{\left(4k+1\right)\left(4k^{2}+1\right)}{4\left(2k^{2}-5k-5\right)}\text{, }y=\frac{\left(2k-1\right)\left(4k+1\right)}{2k^{2}-5k-5}\text{, }z=\frac{2k^{3}+3k^{2}+k+1}{2k^{2}-5k-5}\text{, }&k\neq \frac{1}{2}\text{ and }k\neq \frac{\sqrt{65}+5}{4}\text{ and }k\neq \frac{5-\sqrt{65}}{4}\\x\in \mathrm{R}\text{, }y=0\text{, }z=\frac{8x+1}{2}\text{, }&k=\frac{1}{2}\end{matrix}\right.
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