In this paper, the implementation of Gaussian elimination and Gauss-Jordan reduction are discussed in detailed explanations. There were several results from various research journals compared to comprehend the concepts and practices of both methods. The goal was to analyze the differences of Gaussian elimination and Gauss-Jordan reduction regarding the application, algorithm, complexity, efficiency, problem-solving ability, and stability. As the result, we found that the Gauss-Jordan reduction has lower time efficiency and greater residual (the error in the result) in problem-solving ability. The rests are somewhat similar. In practice, those differences are a substantial consideration in choosing the most suitable method for a particular linear equations’ problem, especially when accuracy and computation time have a significant impact on the result
