good chemistry is complicated, and a little bit messy LW 

PerlMonks 
Re: Solving Simultaneous Equations with Matricesby tsee (Curate) 
on Apr 28, 2004 at 15:08 UTC ( #348854=note: print w/ replies, xml )  Need Help?? 
Another alternative would be to use Math::Symbolic to solve certain classes of equations. The manual of Math::Symbolic::MiscAlgebra has the following on it:
Note that the complexity of Cramer's rule is O(n!) whereas Gaussian Elimination works in O(n^3) as noted by others in this thread. Steffen
In Section
Meditations

