The hole theory is applied to represent the P-V-T-X relations at the phase boundary of the CO2-CH4 and the CO2-N2 systems. As these systems contain super-critical components, Henderson''s approximation for free volume was simplified and adopted for these expanded solutions. An equation of state was derived by introducing two characteristic parameters, which were determined from the heat of vaporization and the saturated densities of liquid and vapor of the pure substance. The equation of state successfully explains the P-V-T-X relations of the above systems with the aid of combining rules for characteristic parameters.