Question

розв’яжіть систему рівнянь

Answer 1

$\displaystyle\bf\\\left \{ {{(x-2)(y-2)xy=9} \atop {xy-x-y=3}} \right.\\\\\\\left \{ {{(xy-2x-2y+4)xy=9} \atop {xy-(x+y)=3}} \right. \\\\\\\left \{ {{\Big[xy-2\cdot(x+y)+4\Big]xy=9} \atop {xy-(x+y)=3}} \right. \\\\\\\left \{ {{\Big[3-(x+y)+4\Big]xy=9} \atop {xy-(x+y)=3}} \right.\\\\\\\left \{ {{\Big[7-(x+y)}\Big]xy=9 \atop {xy=3+(x+y)}} \right. \\\\\\x+y=m\\\\(7-m)\cdot(3+m)=9\\\\21+7m-3m-m^{2}-9=0\\\\m^{2}-4m-12=0 \\\\m_{1} =-2 \ \ , \ \ m_{2} =6$

$\displaystyle\bf\\1) \ m_{1} =-2\\\\x+y=-2 \ \ \Rightarrow \ \ xy=3-2=1\\\\x=-1 \ \ , \ \ y=-1\\\\2) \ m=6\\\\x+y=6 \ \ , \ \ xy=3+6=9\\\\x=3 \ \ , \ \ y=3\\\\\\Otvet \ : \ (-1 \ , \ -1) \ , \ (3 \ ; \ 3)$