This paper proposes two transformations for homogeneous reaction systems with inlet and outlet streams that allow isolating three distinct parts of the state vector, namely, the reaction variants, the reaction invariants but inlet- flow variants, and the reaction and inlet-flow invariants. In the absence of an outlet stream, as in batch and semi-batch reactors, the first transformation leads to the concepts of extents of reaction and extents of inlet flow. For reaction systems with an outlet stream, the second transformation uses key components to decouple the variables and arrive at the new concepts of generalized extents of reaction and generalized extents of inlet flow. These transformations are helpful to compute the reaction invariants for general open homogeneous reaction systems. Furthermore, the energy balance equation is shown to augment the number of reaction invariants by one. The various concepts are illustrated through the analysis of a simulated ethanolysis reaction.