Solution of Systems of Linear Equations Using Triangularization and Backward Substitution

Abstract

Linear equation systems are fundamental concepts in mathematics that play a vital role across various scientific fields. This study aims to examine and analyze solution methods for linear systems using triangularization and backward substitution techniques. The research employs a literature review approach with a qualitative descriptive method, sourcing data from various scientific texts, theses, and relevant journal articles. The results indicate that the triangularization process effectively transforms a linear system into an upper triangular matrix form, simplifying and accelerating the solution process. Subsequently, backward substitution systematically determines variable values starting from the last equation moving backward. The combined use of these methods proves to be effective, structured, and efficient, especially for systems with many variables. A linear system is considered simple if all variable values can be obtained with less effort and faster than before simplification. This research contributes to enhancing the understanding of the mathematical concepts and procedures for solving linear systems and supports the development of numerical algorithms in science and technology fields.