I hope you're well,

I was finding the points of intersection of 
$$
x^2 + (y-1)^2 = 1
\quad \text{and} \quad
y = 1-x^2 
$$
If I rearrange the formula of the circle to 
$$
(y-1)^2 = 1-x^2 
$$
then substitute the second equation to get
$$
(y-1)^2 = y 
$$
I then solve this to get two values of $y$, of which obviously by the symmetry of the problem there can only be one value of $y$. Where has this additional 'solution' come from? Is it because I substituted something that was a quadratic with something that was linear?

Thanks!