Question

Решить систему уравнений  $left { {{xy+ y^{2}+x =5y} atop {x^{2}+xy =6y}} right.$

Answer 1

$xy+y^2+x=5y\ x^2+xy=6y\ \ 5y-y^2-x=6y-x^2\ x^2-y^2=y+x \ x-y=1\ x=1+y\ (1+y)^2+(1+y)y=6y\ 1+2y+y^2+y+y^2=6y\ 2y^2-3y+1=0\ D=1^2\ y_{1}=1\ y_{2}=0.5\ x=2\ x=frac{3}{2}\ x=0\ y=0$