A system of linear algebraic equations consists of multiple linear equations involving the same set of variables. Generally represented in matrix form, these systems are prevalent in diverse fields, including physics, engineering, economics, and computer science. A generic representation of a system with 'n' equations and 'm' variables can be expressed as Ax = B, where A is the coefficient matrix, x is the column vector of variables, and B is the column vector of constants. Linear algebra serves as the backbone of numerous mathematical and scientific disciplines, providing a powerful framework for solving complex problems. One fundamental concept within linear algebra is the system of linear algebraic equations. In this article, we delve into the intricacies of such systems and explore various methods employed for their solution.