Solving a system of non-linear equations has always been a complex issue whereby various methods were carried out. However, most of the methods used are optimization-based methods. This paper has modified the spectral gradient method with the backtracking line search technique to solve the non-linear systems. The efficiency of the modified spectral gradient method is tested by comparing the number of iterations, the number of function calls, and computational time with some existing methods. As a result, the proposed method shows better performance and gives more stable results than some existing methods. Moreover, it can be useful in solving some non-linear application problems. Therefore, the proposed method can be considered an alternative for solving non-linear systems.