$\text{a)}$  

Upraszczamy równania.

$\{\begin{array}{l}xy=\left(2+x\right)\left(y-2\right)\\ 2xy=\left(x-1\right)\left(2y-1\right)+9\end{array}$  

$\{\begin{array}{l}xy=2y-4+xy-2x\mid -xy\\ 2xy=2xy-x-2y+1+9\mid -2xy\end{array}$  

$\{\begin{array}{l}0=2y-4-2x\mid +2x\\ 0=-x-2y+10\end{array}$  

$\{\begin{array}{l}2x=2y-4\mid :2\\ 0=-x-2y+10\end{array}$  

$\{\begin{array}{l}x=y-2\\ 0=-x-2y+10\end{array}$