aspg-21-2350-1791475503 20261008160503 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 23 2 Maissam Jdid Faculty of Science, Damascus University, Damascus, Syria Florentin Smarandache University of New Mexico، Mathematics, Physics and Natural Sciences Division 705 Gurley Ave., Gallup, NM 87301, USA Operations research methods are among the modern scientific methods that have occupied a prominent place among the mathematical methods used in planning and managing various economic and military activities. They have been able to help specialists in developing ideal plans in terms of costs, production, storage, or investment of human energies. One of its most important methods is the method Linear programming, which was built based on the sets of linear equations that represent the constraints for any linear model. Based on the methods for solving the systems of linear equations, researchers were able to prepare algorithms for solving linear models, such as the direct Simplex algorithm and its modifications. After the emergence of neutrosophic science, we found that research methods had to be reformulated. Operations using the concepts of this science, and as a basis and foundation for neutrosophic linear programming. In this research, we will reformulate the systems of linear equations and some methods for solving them using the concepts of neutrosophic to be a basis for any study presented in the field of neutrosophic linear programming. 2024 16 25 2350 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.230202 https://www.americaspg.com/journal/21/article/2350 https://www.americaspg.com/storage/81703625321.pdf