Journal of Generalized Lie Theory and Applications

This paper introduces a new method for solving systems of equations of any order n with m variables by taking the help of row echelon form. Our approach generalizes the solution process by treating each variable as a constant relative to the others within the system. This method leverages the fact that in a given system, each variable has a unique value, allowing it to be considered fixed when solving for another variable. By systematically transforming the system into row echelon form, we can solve complex, high-order, and non-linear systems through a sequence of simplified, linear-like operations. The proposed framework is demonstrated to be effective for various types of equations, providing a versatile and efficient tool for solving intricate systems in mathematics.