  We consider linear elimination of variables in steady state equations of a
chemical reaction network. Particular subsets of variables corresponding to
sets of so-called reactant-noninteracting species, are introduced. The steady
state equations for the variables in such a set, taken together with potential
linear conservation laws in the variables, define a linear system of equations.
We give conditions that guarantee that the solution to this system is
nonnegative, provided it is unique. The results are framed in terms of spanning
forests of a particular multidigraph derived from the reaction network and
thereby conditions for uniqueness and nonnegativity of a solution are derived
by means of the multidigraph. Though our motivation comes from applications in
systems biology, the results have general applicability in applied sciences.
