This document discusses different methods for solving systems of linear equations, including Cramer's rule, elimination methods, and Gaussian elimination. Cramer's rule uses determinants to find the values of variables by dividing the determinant of the coefficients by the primary determinant. Elimination methods remove one unknown using addition or subtraction of equations. Gaussian elimination transforms the coefficient matrix into row echelon form through elementary row operations to solve the system. The document provides examples of applying each method to solve sample systems of linear equations.