I need to solve the system: $$x^2+2xy+y^2-1 = 0$$ where variable is $x$ AND $$x^2 + 2xy = 0$$ where variable is $y$. From the first Ι take discriminant, and end in one solution $x_1 = 1-y$ and another $x_2 = -1-y$.
I am a little confused on the second one. The variable is $y$ so I can't say (?) this is a quadratic equation. So, I end up where $y = -x/2$ or constant $x$ equals $0$? But even if I take $x$ as variable end in the same solution... But even after this, how do I proceed answering the first question? Thanks a lot.
Just plug $x^2 + 2xy=0$ into your first equation. You get $y= 1$ or $y=-1$.
Then plug those two into the solutions you got for $x$. So you get $x=-2$ or $x=0$ or $x=2$.
Then evaluate your solutions. (You'll notice for instance that $x=2,\ y=1$ is NOT a solution, but $x=2,\ y=-1$ is.)