Решите систему x^2 + y^2 - 16 = 2xy x^2 + y^2 - 4 = -2xy

[latex] \left \{ {{x^2+y^2-16=2xy} \atop {x^2+y^2-4=-2xy}} \right. \; \left \{ {{x^2-2xy+y^2=16} \atop {x^2+2xy+y^2=4}} \right. \; \left \{ {{(x-y)^2=16} \atop {(x+y)^2=4}} \right. \; \left \{ {{x-y=\pm 4} \atop {x+y=\pm 2}} \right. \\\\\\ \left \{ {{x-y=4} \atop {x+y=2}} \right. \; ili\; \left \{ {{x-y=-4} \atop {x+y=2}} \right. \; ili\; \left \{ {{x-y=4} \atop {x+y=-2}} \right. \; ili\; \left \{ {{x-y=-4} \atop {x+y=-2}} \right. [/latex]  [latex]1)\; \left \{ {{x-y=4} \atop {2x=6}} \right.  [/latex].[latex] \left \{ {{y=-1} \atop {x=3}} \right. [/latex]  [latex] 2)\; \; \left \{ {{x-y=-4} \atop {2x=-2}} \right. \; \left \{ {{y=3} \atop {x=-1}} \right. \\\\3)\; \; \left \{ {{x-y=4} \atop {2x=2}} \right. \; \left \{ {{y=-3} \atop {x=1}} \right. \\\\4)\; \; \left \{ {{x-y=-4} \atop {2x=-6}} \right. \; \left \{ {{y=1} \atop {x=-3}} \right. \\\\Otvet:\; (3,-1)\; ,\; (-1,3)\; ,\; (1,-3)\; ,\; (-3,1)\; .[/latex]