Как сократить систему до такого вида, чтобы можно было решить способом подстановки или...

Решите задачу:

$\left \{ {{x+y=5-xy} \atop {x^2+y^2=7-xy}} \right. \; \oplus \; \left \{ {x+{y=5-xy} \atop {x^2+y^2+x+y=12-2xy}} \right. \\\\(x^2+y^2+2xy)+x+y-12=0\\\\(x+y)^2+(x+y)-12=0\\\\t=x+y\; ,\; \; t^2+t-12=0\; ,\; \; t_1=-4\; ,\; t_2=3\; (teorema\; Vieta)\\\\\left \{ {{x+y=5-xy} \atop {x+y=3}} \right. \; \; ili\; \; \left \{ {{x+y=5-xy} \atop {x+y=-4}} \right. \\\\\left \{ {{3=5-xy} \atop {x+y=3}} \right. \; ili\; \left \{ {{-4=5-xy} \atop {x+y=-4}} \right.$

$\left \{ {{xy=2} \atop {x+y=3}} \right. \; ili\left \{ {{xy=9} \atop {x+y=-4}} \right. \\\\\left \{ {{x(3-x)=2} \atop {y=3-x}} \right. \; ili\; \left \{ {{x(-4-x)=9} \atop {y=-4-x}} \right. \\\\\left \{ {{x^2-3x+2=0} \atop {y=3-x}} \right. \; ili\; \left \{ {{x^2+4x+9=0} \atop {y=-4-x}} \right. \\\\\left \{ {{x_1=1,\; x_2=2} \atop {y_1=2,\; y_2=1}} \right. \; ili\; \left \{ {{D=16-36<0\; \to \; x\in \varnjthing } \atop {y=-4-x}} \right. \\\\Otvet:\; \; (1,2)\; ,\; (2,1)\; .$