Summary: In this paper, we consider a system of quasi variational inequalities involving two arbitrary mappings. It is shown that the system of quasi variational inequalities is equivalent to the fixed point problem using the projection method. We use this alternative formulation to suggest some new inertial projection methods. The convergence criteria of the new methods is analyzed under some appropriate conditions. Several special cases are discussed as applications of the results. It is interesting problem to consider the implementation of the proposed methods with other similar techniques. The concept of this paper may inspire future research in this area. Results obtained in this paper can be viewed as refinement and improvement of previously known results.