Let me talk about my understanding of the circle system. In this topic, a circle system is a set of all circles that pass through the intersection of two known circles.

Here is the reason for this hypothesis.

We assume that the circulatory system equation is:

x^2+y^2- 1+λ(x^2+y^2+2x)=0( 1)

Suppose two circles a (x 1, y 1) and b (x2, y2) intersect.

Then (1) formula must pass through point A and point B.

The reason for this is the following：

Because A and B are the intersections of two circles, A and B satisfy the equations of two circles.

Take point a as an example,

(x 1)^2+(y 1)^2= 1

(x 1)^2+(y 1)^2=2x 1

Finishing:

(x 1)^2+(y 1)^2- 1=0(2)

(x 1)^2+(y 1)^2-2x 1=0(3)

Obviously, point A also satisfies the equation (1)( (2)+λ(3)).

Similarly, point B can satisfy the equation (1).

Because there are infinitely many circles in the circle system, it is necessary to add some restrictions to determine the equation of the circle. In this problem, it is enough to substitute the coordinates of point A into equation (1) (thus solving λ).