From the liquid-liquid equilibrium (LLE) data of a linear polymer, an investigation of the Sanchez and Lacombe equation of state (SL-EOS) is performed with the goal of describing the swelling of three hydrogels: poly(N-isopropylacrylamide), PNIPA; poly(N-vinyl caprolactam), PVCL; and poly(N-diethylacrylamide), PNDEA. The phantom theory is applied to describe the elastic contribution of the network structure. Using SL-EOS with its binary interaction parameter as a linear temperature function is sufficient to describe the lower critical solution temperature (LCST) of non-cross-linked polymers. The results demonstrate that this function is also suitable for modeling the swelling/shrinking and the transition temperature of the corresponding hydrogel. We demonstrate that a simple mechanical model and a simple EOS are sufficient to adequately describe nonelectrolyte hydrogel swelling using LLE data and only one piece of swelling data. In addition, the pressure effects on the hydrogel swelling are analyzed without the need for new parameter estimation, an analysis scarcely found in the literature.