The semi-ideal solution theory has been presented to describe the changes in thermodynamic properties accompanying the process of mixing the nonideal electrolyte solutions M(i)X(i)-(NY)sat-H2O (i = 1 and 2) at constant activities of NY and H2O, including concentration, chemical potential, activities of all M(i)X(i), Gibbs free energy, enthalpy, entropy, thermal properties, and volumetric properties. The theory states that, under the conditions of equal activities of NY and H2O, the average hydration numbers characterizing the ion-solvent interactions have the same values in the mixture as in the subsystems and the process of mixing these nonideal electrolyte solutions is as simple as that of mixing the ideal solutions if the contributions from the ion-ion interactions to the solvent activity are assumed to be the same in the mixture as in its subsystems, which has been justified by the calculations of the Pitzer equation. Therefore, a series of novel linear equations are established for the thermodynamic properties accompanying the process of mixing these nonideal solutions as well as mixing the ideal solutions M(i)X(i)-(NY)sat-H2O (i = 1 and 2) of equal mole fractions of NY and H2O. From these equations, the widely applied empirical Zdanovskii's rule is derived theoretically, and the important constant in the McKay-Perring equation under isopiestic equilibrium is determined theoretically, which has been substantiated by comparisons with the experimental results for 18 mixtures reported in the literature. Isopiestic measurements have been made for the systems BaCl2-LaCl3-H2O, NaCl-BaCl2-LaCl3-H2O, and NaCl-LaCl3-BaCl2.2H2O(sat)-H2O at 298.15 K. The results are used to test the novel linear concentration relations, and the agreement is excellent. The novel predictive equation for the activity coefficient of M(i)X(i) in M1X1-M2X2-(NY)sat-H2O has been compared with the calculations of the Pitzer equation, and the agreement is good.