There are numerous direct techniques available for solving simultaneous equations, such as the Elimination Method, the Substitution Method, the Graphical Method, and Matrix Methods, among others. In this paper, we focus on the Paravartya rule (also known as the cross-multiplication method), which was introduced by Jagadguru Swami Sri Bharati Krishnna Tirathji Maharajaas a way to solve systems of two linear equations. We then demonstrate how this rule can be expanded and applied to solve systems of n linear equations by providing several examplesWhile this method is not a simple, one-step procedure, it is generally faster and more efficient than traditional approaches, offering a shorter and more streamlined solution for solving systems of linear equations.

Paravartya Rule (Cross-Multiplication Method), Extension to n Equations, Efficiency