Given three equations as follow: $$ B_x^2+B_y^2=4 \\ (B_x-D_x)^2+(B_y-D_y)^2=9\\ (D_x-4)^2+D_y^2=4 $$ How to find the range of each unknown so these equations can be valid?
Is there any analytical or numerical method to solve this problem?
Any general method to solve the system is up to n equations and n+1 unknowns?
Hint: These are all equations describing circles. The equation of a circle is: $(x-x_0)^2+(y-y_0)^2=r^2$. The point $(x_0,y_0)$ is the center of the circle and $r$ is the radius of the circle.
E.g. $B_x^2+B_y^2=4$, describes all points on a circle with the center $(0,0)$ and the radius $r=2$. So $-2\leq B_x \leq 2$ and $-2\leq B_y \leq 2$.
If you want the exact range, you will have to solve the system of equations.