A Formal Way to Find the Number of Independent Equations

In the previous examples we have found the number of independent chemical equations by intuition or knowledge of the system. This works well for simple systems, but is harder and more umeliable for complex ones. Of the various algorithms for doing this, the simplest reliable one seems to be the following  

Write the formulas for the formation of all the compounds in the species hst from the elements. 

Algebraically eliminate those elements that do not appear in the species list. 

Example 15.8 Determine the maximum number of balanced chemical equations that exist among CaCOa, CaO, and CO2. 

This set of species, the subject of Examples 15.4 and 15.5 is chosen here to illustrate the process. First we write 

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