Система уравнении x²-2xy+y²=xy-1; x-y=1

[latex] \left \{ {{x^2-2xy+y^2=xy-1} \atop {x-y=1}} \right. \; \left \{ {{(x-y)^2=xy-1} \atop {x-y=1}} \right. \; \left \{ {{1=xy-1} \atop {x-y=1}} \right. \; \left \{ {{xy=2} \atop {x-y=1}} \right. \; \left \{ {{x(x-1)=2} \atop {y=x-1}} \right. \\\\\\ \left \{ {{x^2-x-2=0} \atop {y=x-1}} \right. \; \left \{ {{x_1=2,\; x_2=-1\; (teor.\; Vieta)} \atop {y_1=1,\; y_2=-2}} \right. \; \Rightarrow \; \; Otvet::\; (2,1),\; (-1,-2).[/latex]