An extension of the Gibbs-Duhem equation appropriate for a multicomponent fluid containing a solvent, a simple electrolyte, and an arbitrary number of cosolute components is proposed. The general formula is applied to two different systems: (i) a primitive model +1:-1 electrolyte in mixture with a neutral cosolute component and (ii) a mixture of primitive model +1:-1 and +2:-1 electrolytes (cosolute) with a common anion. The mean spherical and hypernetted chain integral equation approximations are used to calculate thermodynamic quantities such as the osmotic coefficient of the solution and the activity coefficients of various species. The mean activity coefficient of the principal solute, which is in this study the +1:-1 electrolyte, is calculated directly using the mean spherical and hypernetted chain integral equation theories or via the extended version of the Gibbs-Duhem equation. The calculations utilizing the two different routes are in agreement, providing a numerical check on the analytical derivations.