The fundamental property of electrolytic systems involved with linear combination f12 = 2∙f(O) – f(H) of elemental balances: f1 = f(H) for Y1 = H, and f2 = f(O) for Y2 = O, is presented. The dependency/independency of the f12 on Charge Balance (f0 = ChB) and other elemental and/or core balances fk = f(Yk) (k = 3,…,K) is the general criterion distinguishing between non-redox and redox systems. The f12 related to a redox system is the primary form of a Generalized Electron Balance (GEB), formulated for redox systems within the Generalized Approach to Electrolytic System (GATES) as GATES/GEB ⊂ GATES. The set of K balances f0,f12,f3,…,fK is necessary/ sufficient/needed to solve an electrolytic redox system, while the K-1 balances f0,f3,…,fK are the set applied to solve an electrolytic non-redox system. The identity (0 = 0) procedure of checking the linear independency/ dependency property of f12 within the set f0,f12,f3,…,fK (i) provides the criterion distinguishing between the redox and non-redox systems and (ii) specifies Oxidation Numbers (ONs) of elements in particular components of the system, and in the species formed in the system. Some chemical concepts, such as oxidant, reductant, oxidation number, equivalent mass, stoichiometry, perceived as derivative within GATES, are indicated. All the information is gained on the basis of the titration Ce(SO4)2 (C) + H2SO4 (C1) + CO2 (C2) ⇨ FeSO4 (C0) + H2SO4 (C01) + CO2 (C02), simulated with use of the iterative computer program MATLAB.