# Most effective way to solve system of non-linear equations with unique set of roots [closed]

What is the most effective way to solve a system of non-linear equations if we know for sure that they have a unique set of roots?

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## closed as too broad by Jonas Meyer, daw, mrf, Najib Idrissi, KrishMar 25 at 9:10

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs. If this question can be reworded to fit the rules in the help center, please edit the question.

This question seems too vague to me –  Kaster Dec 13 '12 at 8:42
It depends on the system of non-linear equations. –  copper.hat Dec 13 '12 at 8:44
In practical terms, I would say: ask Mathematica for the answer. –  user108903 Dec 13 '12 at 9:01

I think that all mathematicians would say that it is very important to develop a toolbox of problem solving approaches because all problems have unique subtleties.

Being able to look at problems from different angles is very important as there is typically never a one-size fits all across all problems (there are cases where generalizations are possible in some areas).

However, with non-linear equations, all sorts of strange things can happen. For your question, you might approach it in an algorithmic way where you try the standard approaches and see if there is a closed form solution, try graphing, transformations, numerical methods...

There are many wonderful books on the subject and there are programs you can use (both commercial and free).

If you could provide a specific example of the sort of problem you are actually solving, the group could perhaps provide some more specific details regarding an approach.

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Nice, Amzoti! Great encouragement, and effort expended to answer a very vague question! –  amWhy May 15 '13 at 0:32
@amWhy: Never heard back and have never see the OP back on. :-) –  Amzoti May 15 '13 at 0:33