Sistemas de equações não lineares no ensino médio um estudo significativo

Abstract

In this work, we investigate the mathematical challenges of moving beyond linear relationships by introducing nonlinear systems of equations as a fascinating and widely applicable class of problems. This work was motivated by a deeper analysis of this scenario and the discovery of a significant gap in both Portuguese and foreign language textbooks dedicated to solving nonlinear systems of equations. The main objective is to present analytical methods, theorems, properties, and efficient strategies for solving these systems in high school. We aim not only to fill this identified educational gap but also to demonstrate the practical applicability of these concepts to specific problem-solving situations, making the content more concrete and relevant to high school students. The methodology emphasizes a clear and accessible approach that not only provides a solid understanding of the underlying theory but also presents practical methods that are directly applicable in classroom environments. Analytical methods for solving systems of equations emerge as valuable resources for high school students, laying a solid preparatory foundation for tackling more complex mathematical challenges such as participation in Olympiads, military entrance exams, and other competitions. These tools not only strengthen students’ conceptual understanding but also empower them to effectively tackle challenging mathematical problems, promoting continuous improvement in their academic development.