$\left \{ {{x(x-3y)+y(y+x)=0} \atop {\sqrt[]{x}\sqrt[]{y-2}=1 }} \right.$
⇔$\left \{ {{x^2-3xy+y^2+xy=0} \atop {\sqrt[]{xy-2x}=1 }} \right.$
⇔$\left \{ {{x^2-2xy+y^2=0} \atop {xy-2x=1 }} \right.$
⇔$\left \{ {{(x-y)^2=0} \atop {xy-2x=1 }} \right.$
⇔$\left \{ {{x-y=0} \atop {xy-2x=1 }} \right.$
⇔$\left \{ {{x=y} \atop {y^2-2y=1 }} \right.$
⇔$\left \{ {{x=y} \atop {y^2-2y+1=2 }} \right.$
⇔$\left \{ {{x=y} \atop {(y-1)^2=2 }} \right.$
⇔$\left \{ {{x=y} \atop {y-1=±\sqrt[]{2} }} \right.$
⇔$\left \{ {{x=y=±\sqrt[]{2}+1} \atop {y=±\sqrt[]{2}+1 }} \right.$
Vậy....
