$hpt<=>\begin{cases}2x+2y+2xy=6 \\ 2y^2+2y^2=4 \end{cases}$$=>2x^2+2y^2-2x-2y-2xy+2=0$$<=>(x-1)^2+(y-1)^2+(x-y)^2=0$$<=>x=y=1$
$hpt<=>\begin{cases}2x+2y+2xy=6 \\ 2y^2+2y^2=4 \end{cases}$$=>2x^2+2y^2-2x-2y-2xy+2=0$$<=>(x-1)^2+(y-1)^2+(x-y)^2=0$
$hpt<=>\begin{cases}2x+2y+2xy=6 \\ 2y^2+2y^2=4 \end{cases}$$=>2x^2+2y^2-2x-2y-2xy+2=0$$<=>(x-1)^2+(y-1)^2+(x-y)^2=0$
$<=>x=y=1$