In this work, we demonstrate that tracing the vapor-liquid equilibria for binary mixtures also includes all the information needed to obtain the three-phase line if one is present. This simple observation serves as a launching point for calculation of the liquid-liquid equilibrium and three-phase equilibria, even when one component is supercritical. We close with the demonstration of the automatic construction of an isothermal pressure-composition figure, a capability enabled by solving for the three-phase state. The scripts in the Supporting Information demonstrate in detail how the method is applied.