For a bit of background on this problem and the problems that can arise when solving sets of equations, check out Numerical recipes for C (or any of the other languages such as Fortran77, Fortran90 and C++ although the latter is not available online. The book is quite nice to read, actually.

A nice book that's not available online is Real computing made real by Forman S. Acton.

Just my 2 cents, -gjb-