$$PUTy=2x-1$$
$\left\{\begin{matrix}P=-\frac{1-2x}{TUy}\text{, }&y\neq 0\text{ and }T\neq 0\text{ and }U\neq 0\\P\in \mathrm{C}\text{, }&\left(y=0\text{ or }T=0\text{ or }U=0\right)\text{ and }x=\frac{1}{2}\end{matrix}\right.$
$\left\{\begin{matrix}T=-\frac{1-2x}{PUy}\text{, }&y\neq 0\text{ and }U\neq 0\text{ and }P\neq 0\\T\in \mathrm{C}\text{, }&\left(y=0\text{ or }U=0\text{ or }P=0\right)\text{ and }x=\frac{1}{2}\end{matrix}\right.$
$\left\{\begin{matrix}P=-\frac{1-2x}{TUy}\text{, }&y\neq 0\text{ and }T\neq 0\text{ and }U\neq 0\\P\in \mathrm{R}\text{, }&\left(y=0\text{ or }T=0\text{ or }U=0\right)\text{ and }x=\frac{1}{2}\end{matrix}\right.$
$\left\{\begin{matrix}T=-\frac{1-2x}{PUy}\text{, }&y\neq 0\text{ and }U\neq 0\text{ and }P\neq 0\\T\in \mathrm{R}\text{, }&\left(y=0\text{ or }U=0\text{ or }P=0\right)\text{ and }x=\frac{1}{2}\end{matrix}\right.$