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One of the most important problems in Applied Mathematics, is the solution of linear equations systems. Gaussian elimination is the main procedure in order to solve this problem with a computer. It was also the first algorithm for which an analysis of rounding errors was made.

From the point of view of Theorical Algebra, given a system of linear equations, there are different ways of obtaining equivalent systems until arriving at a reduced system that allows us, if necessary, to solve it.

In this paper, the different methodologies used to explain the methods related to Gaussian elimination are analyzed, both in the pre-university studies and in the degree studies in regulated education in Spain. From a survey carried out on students who study the subject of Numerical Analysis in the first year of industrial engineering in the Politechnical School of Engineering of Gijón (University of Oviedo), the differences of procedure existing in the use of the Gaussian method are verified.

The above expressed leads us to propose specific changes in the treatment of the resolution methods of linear equations systems that are studied in the Baccalaureate.