Sistemas lineares: Uma sequência didática para o Ensino Médio e aplicações

Abstract

In this research, we present a study about systems of linear equations, considering a didactic sequence that can be used in high school classes, especially in second-year classes. Originally, the text brings a brief reflection about the teaching process of the linear system, emphasizing the great importance of this content to the various areas of human knowledge. The definitions and main results about linear order systems of 2×−2, 3×−2, 2×−3 and 3×−3 will be presented. On this occasion we will emphasize the geometric interpretation of each equation that constitutes the system, as well as the utilization of the scaling technique and application of the post theorem, searching for the solution of each explored system. For this study, we will consider a method that involves algebraic and geometric aspects, exploring the existing relationships between the system and relative positions of straight lines or planes that represent the equations, as well as the relationships among the coefficients. Finally, we propose activities, showing the presence of linear systems in different situations, so that the reader, with the help of GeoGebra, can interpret graphically the solution of the system and after that apply the techniques and procedures studied throughout this study to solve the system.