Question

розв'яжіть систему рівнянь 2ху + х = 5 2ху + у = 6

Answer 1

$\displaystyle\bf\\-\left \{ {{2xy+x=5} \atop {2xy+y=6}} \right.\\---------\\x-y=-1\\\\x=y-1\\\\2y\cdot(y-1)+y=6\\\\2y^{2} -2y+y=6\\\\2y^{2} -y-6=0\\\\D=(-1)^{2} -4\cdot 2\cdot(-6)=1+48=49=7^{2} \\\\\\y_{1} =\frac{1-7}{4}=-1,5 \\\\\\y_{2}=\frac{1+7}{4}=2\\\\\\x_{1}=-1,5-1=-2,5\\\\\\x_{2}=2-1=1\\\\\\Otvet \ : \ (-2,5 \ , \ -1,5) \ , \ (1 \ ; \ 2)$