Решите систему уравнений 2(x+y)-xy=4 2xy+x+y=-18

[latex]\left \{ {{2(-2xy-18)-xy=4} \atop {x+y=-2xy-18}} \right. \left \{ {{-4xy-36-xy=4} =\ \textgreater \ 5xy=-40 =\ \textgreater \ xy=-8 \atop {x+y=16-18=-2}} \right. [/latex]   [latex]\left \{ {{(-2-y)y=-8 \atop {x=-2-y}} \right. \left \{ {{-2y-y^{2} =-8 =\ \textgreater \ y^{2}+2y-8=0 \atop {x=-2-y}} \right.[/latex] Решаем первое уравнение [latex]y^{2}+2y-8=0 [/latex] D=4+32=36  [latex] y_{1}= \frac{-2+6}{2}=2; y_{2}= \frac{-2-6}{2}=-4[/latex] Тогда получаем 2 решения системы [latex]\left \{ {{ y_{1}=2 \atop {x_1=-2-y=-4}} \right. \left \{ {{ y_{2}=-4 \atop {x_2=-2-y=2}} \right.[/latex]