Abstract This paper aims to introduce some prevalent techniques which have been used to solve linear systems. Firstly, we introduce the simplest method: how to eliminate variables in which the original systems would not be changed. We then introduce Gaussian eliminations, which work on the augmented matrix derived from a linear system. To the end, we present Cramer’s rule, which computes the solution to a linear system based on matrix determinants. These methods have their application scenarios. For instance, elim…