In this paper linear equations are discussed in detail along with elimination method. Guassian elimination and Guass Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Guassian elimination and Guass Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theorey and forms of Guassian elimination through which the performance of Guass Jordan and Guassian elimination can be measured.