х^2+ху+у^2=7
х^2-у^2=3
x-y=u
x+y=v
x=(u+v)/2
y=(u-v)/2
{3v^2+u^2=28
{uv=3
способ подстановки
u=3/v
биквадратное уравнение
3v^4-28v^2+9=0
D=784-108=676
v^2=1/3 или v^2=9
v_(1)= - 1/sqrt(3); v_(2)=1/sqrt(3); v_(3)=-3;v_(4)=3
u_(1)=-3sqrt(3);u_(2)=3sqrt(3);u_(3)=-1;u_(4)=1
x_(1)=(-3sqrt(3))/2 - (1)/(2sqrt(3))
x_(2)=(3sqrt(3))/2+(1)/(2sqrt(3))
x_(3)=-2
x_(4)=2
y_(1)=(-3sqrt(3))/2+(1)/(2sqrt(3))
y_(2)=(3sqrt(3))/2-(1)/(2sqrt(3))
y_(3)=2
y_(4)=-1