In order to calculate the thermodynamic properties of a two-dimensional Lennard-Jones system, we have carried out computer simulations to obtain its radial distribution function. The relative dependence between the repulsive and attractive intermolecular forces on the thermodynamics of these systems is modeled through the separation of the intermolecular potential proposed by Weeks, Chandler and Andersen. We simulated a large number of states and we obtain exact expressions for the thermodynamic properties by fitting to an analytical expression. The results extrapolated to the critical region permit us to propose a simple method to determine the critical properties of these systems, Despite the approximate nature of this method, its predictions are in agreement with previously published results for the full Lennard-Jones system. When the intensity of the attractive forces relative to the repulsive forces is changed, we found that the critical point varies linearly. These results could be important in applications where the repulsive forces have a different intensity such as is the case of the Lennard-Jones neutral molecules and in the adsorption of rare gases under an electric field caused by a solid surface.