$\left\{\begin{matrix}p=-\frac{qx-x-y+qz}{y+z}\text{, }&y\neq -z\\p\in \mathrm{R}\text{, }&\left(y=q\left(-\frac{x\left(q-1\right)}{q+1}+x\right)-x\text{ and }z=-\frac{x\left(q-1\right)}{q+1}\text{ and }q\neq -1\right)\text{ or }\left(y=-z\text{ and }x=0\text{ and }q=-1\right)\end{matrix}\right.$

$\left\{\begin{matrix}q=-\frac{pz-y+py-x}{x+z}\text{, }&z\neq -x\\q\in \mathrm{R}\text{, }&\left(x=0\text{ and }z=0\text{ and }p=1\right)\text{ or }\left(z=-x\text{ and }y=\frac{x\left(p+1\right)}{p-1}\text{ and }p\neq 1\right)\end{matrix}\right.$