Question

Помогите пожалуйста!
Решите систему уравнений {у+2ху=7; х+2ху=9

Answer 1

$left { {{y+2xy=7} atop {x+2xy=9}} right. left { {{2xy=7-y} atop {x(2y+1)=9}} right. left { {{x=frac{7-y}{2y}} atop {frac{7-y}{2y}(2y+1)=9}} right. \frac{7-y}{2y}(2y+1)=9|cdot2y\(7-y)(2y+1)=18y\14y+7-2y^2-y-18y=0|cdot(-1)\2y^2+5y-7=0\D=25+56=81=9^2\y_{1,2}=frac{-5pm9}{4}=left |{ {{1} atop {-3,5}} right.$

$left[begin{gathered}left{begin{gathered}x+2xy=9 hfill\y=1hfill\end{gathered}right.hfill\left{begin{gathered}x+2xy=9hfill\y=-3,5hfill\end{gathered}right.hfill\end{gathered}right.$ $left[begin{gathered}left{begin{gathered}x=3 hfill\y=1hfill\end{gathered}right.hfill\left{begin{gathered}x=1,5hfill\y=-3,5hfill\end{gathered}right.hfill\end{gathered}right.$

Ответ: $(3;1);(1,5;-3,5)$