We present both fluorescence spectroscopy and integral equation studies of supercritical and subcritical fluid mixtures that demonstrate the possibility of a solute being preferentially solvated by either of the components in the mixture dependent on the pressure, along a given isotherm. The fluorescence studies use the relatively nonpolar probe pyrene to estimate the degree of preferential solvation in mixtures of CO2 and CHF3. In a mixture of 15 mol % CHF3 in CO2, the CHF3 preferentially solvates the probe at reduced densities greater than about 1.3. However, for reduced densities between 0.7 and 1.3 the solvent strength is very close to that of pure CO2, indicating a depletion of the CHF3 in the solvent shell around the solute. This general behavior is confirmed by integral equation calculations for ternary mixtures. Local compositions of the solvents around a dilute solute are calculated from the pair correlation functions. These are obtained using the numerical method of Labik-Gillan for solution of the Ornstein-Zernike equation with the Percus-Yevick closure. We investigate the influence of the size and energy parameters of the solvents on the degree and nature of the preferential solvation and demonstrate the interesting solvation behavior that can occur as one traverses from low-density gas to high-density supercritical fluid.