Stoichiometric analysis uses matrix algebra to deduce the constraints implicit in metabolic networks. When applied to simple networks, it can often give the impression of being an unnecessarily complicated way of arriving at information that is obvious from inspection, for example, that the sum of the concentrations of the adenine nucleotides is constant. Applied to a more complicated example, that of glycolysis in Trypanosoma brucei, it yields information that is far from obvious and may have importance for developing therapeutic ways of eliminating this parasite. Even in simplified form, the network contains nine reactions or transport steps involving 11 metabolites. This immediately shows that there must be at least two stoichiometric constraints, and indeed two can be recognized by inspection: conservation of adenine nucleotides and conservation of the two forms of NAD. There is, however, a third, which involves eight different phosphorylated intermediates in non-obvious combinations and is very difficult to recognize by inspection. It is also difficult to recognize by inspection that no fourth stoichiometric constraint exists. Gaussian elimination provides a systematic way of analysing a network in such a way that all the stoichiometric relationships that it contains emerge automatically.