$\left\{ \begin{array}{l} (x-1)(y-1)(x+y-2)=0\\x^2+y^2-2x-2y-3=0 \end{array} \right.$$\Leftrightarrow \left\{ \begin{array}{l} (x-1)(y-1)(x-1+y-1)=0\\ (x-1)^2+(y-1)^2-5=0\end{array} \right.$
Đặt $x-1=a; y-1=b$, ta có:
$\left\{ \begin{array}{l} ab(a+b)=0\\ a^2 + b^2 -5 =0 \end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l} (a+b)^2 -2ab=5 \\ab(a+b)= 0\end{array} \right.$
Dễ rồi chứ!!