pt $\Leftrightarrow x^{3}+y^{3}+2xy(x+y)-3(x^{2}+y^{2})+3(x+y)-4xy-2=0$ $ \Leftrightarrow (x-1)^{3} +(y-1)^{3}+2xy(x+y-2)=0$
Đặt $x-1=a;y-a=b$
$\Rightarrow a^{3}+b^{3}+2(a+1)(b+1)(a+b)=0$
$\Leftrightarrow (a+b)(a^{2}-ab+b^{2}+2(a+1)(b+1))=0$
$\Leftrightarrow (a+b)(a^{2}+ab+b^{2}+2a+2b+2)=0$
ta có $(....)=(a+\frac{b+2}{2})^{2}+(\frac{b+2}{2})^{2}+\frac{b^{2}}{2}>0$
$\Rightarrow a+b=0 \Rightarrow x+y=2$