You are welcome!

]]>Okay. Thanks!

]]>After 30 iterations, I get (80.3416234530054, 86.8627875987953).

Wonderful!

Start the process by putting x = 1.0 and y = 1.0

Now run the next two equations 1 time:

Tell me what you get for x and y.

]]>Yes, followed till there.

]]>sage: import scipy seems to load a bunch of root finders.

But let me see what I can do with those equations by hand. Please hold on.

Okay do this, start with the first equation:

Subtract

from both sides. You get

Multiply both sides by

You get.

Divide through by:

-2300

You get:

Now you have x on the right by itself. Do the same moves with the second equation to get a y by itself on the right.

Do you follow up to here?

]]>Ok, thanks.

Sage couldn't solve it. Is there any numerical method?

These are the two partial derivatives set to 0. Mathematica can now solve them numerically. Sage must have a similar command.

]]>I guess numerical solution is good enough for this problem. After all, numbers is what we need.

But I don't know the numerical solution either. Which are the derivatives to be considered to solve?

]]>I also do not know of any algorithm to solve it. I would form the distance equations. Take the partial derivatives and set them to 0 and solve the system of equations numerically.

]]>