$\left\{\begin{matrix}a=\frac{x\left(y+1\right)}{y-1}\text{, }&x\neq 0\text{ and }y\neq 1\\a\neq 0\text{, }&x=0\text{ and }y=1\end{matrix}\right.$

$\left\{\begin{matrix}x=\frac{a\left(y-1\right)}{y+1}\text{, }&a\neq 0\text{ and }y\neq -1\\x\neq 0\text{, }&a=0\text{ and }y=-1\end{matrix}\right.$