Question

Розв'язати систему {x+y+xy=11
{x+y-xy=1

Answer 1

$\left \{ {{x+y+xy=11} \atop {x+y-xy=1}} \right.\; \oplus \ominus \left \{ {{2x+2y=12} \atop {2xy=10}} \right.\; \left \{ {{x+y=6} \atop {xy=5}} \right.\; \left \{ {{y=6-x} \atop {x(6-x)=5}} \right.\; \left \{ {{y=6-x} \atop {x^2-6x+5=0}} \right.\\\\\left \{ {{y_1=5\; ,\; y_2=1} \atop {x_1=1\; ,\; x_2=5}} \right. \; \; \Rightarrow \; \; \; \underline {(1,5)\; ,\; \; (5,1)\; }.$