Find all real solutions to the following system of nonlinear

Find all real solutions to the following system of non-linear equations:

x²+xy+y²=3

x²-3xy+y²=11

given

x^2+xy+y^2=3 -------->1st

x^2-3xy+y^2=11 --------->2nd

in the 1st equation take \'xy to the right hand side

then we get x^2 +y^2 = 3 -xy

plug x^2+y^2 value in equation 2

then we get

3 - xy -3xy =11

3 -4xy =11

-4xy =11-3

-4xy =8

xy =-2

y = -2/x

plug this \'y\' value in equation1

x^2 -x (2/x) +(4/x^2) =3
x^4 -2x^2 +4= 3x^2

x^4 -5x^2 +4=0
x= 1,-1 satisfy this
x^4 -5x^2 +4 can be wrriten as (x^2 -1) (x^2 -4)

so (x^2 -1) (x^2 -4) =0

x = 1, -1 ,2,-2

now find put y value by y = -2/x

when x=1 y =-2 solution is (1,-2)

when x=-1 y =2 sloution is (-1,2)

when x=2 y =-1 solution is (2,-1)

when x=-2 y=1 solution is(-2,1)