Linear equation is an important part of mathematics. A System of linear equation is a set of two or more linear equations. Solving system of linear equations with minimum cost is a well defined problem and studied from long times ago. This works goal is to solve the system of linear equations in a cost effective way and this goal is achieved successfully by minimizing the execution time of the proposed algorithm. There are various approaches to solve the system of linear equations. "A New Method for Solving the System of Linear Equations", is a work which aims to find a new approach different from the traditional approaches in a cost effective way.