Question 13938
What you have here are the equations of two circles. The standard form is: {{{(x-h)^2 + (y-k)^2 = r^2}}}
The first has its center at (1, 0) and its radius is 1.
The second has its center at (0, 1) and its radius is also 1.

These two circles intersect at only two points which you have correctly identified.

How are you getting a third point of intersection?
Graph the two equations and you will see the two points of intersection.