Помогите решить систему:[latex] \sqrt{x+y-6} = \sqrt{x-y-2} [/latex] [latex] x^{3} + y^{3} = 3x+3y[/latex]

[latex] \left \{ {{\sqrt{x+y-6}=\sqrt{x-y-2}} \atop {x^3+y^3=3x+3y}} \right. \; \left \{ {{x+y-6=x-y-2} \atop {(x+y)(x^2-xy+y^2)=3(x+y)}} \right. \; \left \{ {{2y=4} \atop {x^2-xy+y^2=3}} \right. \\\\ \left \{ {{y=2} \atop {x^2-2x+1=0}} \right. \; \left \{ {{y=2} \atop {(x-1)^2=0}} \right. \; \left \{ {{y=2} \atop {x=1}} \right. [/latex] [latex]x+y-6 \geq 0,y \geq -x+6,2 \geq -1+6\; (neverno)\\\\x-y-2 \geq 0,y \leq x-2,2 \leq -1-2\; (neverno)[/latex] нет решений