Question

Решите систему уравнений left { {{x-xy=-3} atop {y+xy=8}} right. [/tex]

Answer 1

$x-xy=-3, y+xy=8\ x(1-y)=-3, xy=8-y\ x=- frac{3}{1-y} = frac{3}{y-1} , x= frac{8-y}{y} \ frac{3}{y-1} = frac{8-y}{y} \ (8-y)(y-1)=3y\ 8y-8-y^2+y-3y=0\ -y^2+6y-8=0\ y^2-6y+8=0\ D=6^2-4*1*8=36-32=4\ y_1= frac{6+2}{2} =4\ y_2= frac{6-2}{2} =2\ x_1= frac{8-4}{4} =1\ x_2= frac{8-2}{2} =3\ Answer: (1;4), (3;2)$