We introduce a method of calculating emergy that requires only ordinary algebra without any reliance on special rules to account for co-production. This is accomplished by using an intermediate computation "co-emergy", and treating co-production as a problem of scale. In addition, we compare emergy calculations using inputs to the system with emergy calculations using what was used up in the system. It is shown that this can lead to slightly different results. We show how these methods can be used to compute emergy in systems at steady state, with imports and exports and with changes in stocks. These techniques allow direct comparison of competitive species, industries, or technologies using standard methods of linear algebra. It also enables us to include the efficiencies of various processes explicitly, which can help in the formulation and testing of conjectures about the relationships between emergy and local and system-wide efficiencies.