We describe a canonical form of electrolyte solution systems for the mathematical interpretation of solidliquid equilibrium. The canonical form is obtained from the analysis of the algebraic structure of electrolyte solution systems and the Karush-Kuhn-Tucker (KKT) conditions for the minimization of the total Gibbs free energy. As a result, the mathematical role of solid species in the solid-liquid equilibrium problem is explained as a Lagrange multiplier of a sort of the linearly constrained optimization problem. This finding will add to the development of an efficient numerical algorithm for the simulation of electrolyte solution systems.