There are many methods to solving linear systems of equations (provided one has n equations with m unknowns where m is less than n).  However, certain methods have advantages over other methods.  Say we are presented with two equations with two unknowns.  One could solve the system by means of substitution, elimination, Gauss-Jordan elimination, or even guessing (although I would not recommend the last one).  As one is presented with systems that have a greater number of equations and a greater number of unknowns, substitution and elimination can be time consuming.  In cases as such, one could employ the Gauss-Jordan Elimination method to solve for the unknowns.  However, in such a method, one is prone to computational mistakes if one is not careful and this method can be time consuming. 

Kramer’s Rule is a formula for solving a system of n equations with n unknowns and while it is of minor interest concerning computational methods, it is interesting when studying the mathematical properties of a system.