The Linear Equation System is often used in solving problems - completion of electrical circuits. The linear equation can be solved using the GaussJordan Elimination Method. The procedure for the Gauss-Jordan elimination method is to transform linear into an augmentation matrix (A|B), then convert matrix A to an identity matrix by reducing the augmentation matrix. To calculate m equations and n independent variables by unknown number of a large and complex system, it takes a long time and is not efficient. The implementation of the Gauss-Jordan Elimination method using the Scilab Program can help complete a large and complex Linear Equation System in a fast and accurate way.