In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an example of solving a system of linear equations. First, we present an example that we both use in our freshman algebra classes for modeling and problem solving and in our linear algebra class. Then we continue by giving a mathematical modeling algorithm for balancing the more complicated "oxidation-reduction" ("redox") equations using a system of linear equations.