Solve {l}{2x-yz=1}{a=4x+3y+2z}{b=6x+4y-4}{text{Solvefor}c,dtext{where}}{c=a}{d=b}

$$\left. \begin{array} { l } { 2 x - y z = 1 }\\ { a = 4 x + 3 y + 2 z }\\ { b = 6 x + 4 y - 4 }\\ { \text{Solve for } c,d \text{ where} } \\ { c = a }\\ { d = b } \end{array} \right.$$

Solve for x, y, z

$$\left\{\begin{matrix}x=\frac{b\sqrt{9a^{2}-12ab+4b^{2}-8b-8}+3ab-2b^{2}+4\sqrt{9a^{2}-12ab+4b^{2}-8b-8}+12a-24b-16}{6\left(\sqrt{9a^{2}-12ab+4b^{2}-8b-8}+3a-2b\right)}\text{, }y=\frac{4\left(b+1\right)}{\sqrt{9a^{2}-12ab+4b^{2}-8b-8}+3a-2b}\text{, }z=\frac{\sqrt{9a^{2}-12ab+4b^{2}-8b-8}+3a-2b-16}{12}\text{, }&b=d\text{ and }a=c\text{ and }\left(arg(-\left(3c+2\right))\geq \pi \text{ or }d\neq -1\right)\text{ and }\left(c\neq -\frac{2}{3}\text{ or }d\neq -1\right)\\x=\frac{-b\sqrt{9a^{2}-12ab+4b^{2}-8b-8}+3ab-2b^{2}-4\sqrt{9a^{2}-12ab+4b^{2}-8b-8}+12a-24b-16}{6\left(-\sqrt{9a^{2}-12ab+4b^{2}-8b-8}+3a-2b\right)}\text{, }y=\frac{4\left(b+1\right)}{-\sqrt{9a^{2}-12ab+4b^{2}-8b-8}+3a-2b}\text{, }z=\frac{-\sqrt{9a^{2}-12ab+4b^{2}-8b-8}+3a-2b-16}{12}\text{, }&b=d\text{ and }a=c\text{ and }\left(arg(3c+2)\geq \pi \text{ or }d\neq -1\right)\text{ and }\left(c\neq -\frac{2}{3}\text{ or }d\neq -1\right)\\x=\frac{-12c-5}{6}\text{, }y=3c+2\text{, }z=-\frac{4}{3}\approx -1.333333333\text{, }&b=-1\text{ and }a=c\text{ and }d=-1\end{matrix}\right.$$