When an electric circuit is intended to determine the electric currents or when it is intended
to balance certain chemical reactions, or when it is intended to study the flow of traffic in
a particular path, the theory of systems of linear equations becomes essential for such end.
It is a fundamental part of Linear Algebra, being support for several theories in Modern
Mathematics. Physics, Chemistry, Engineering and Biology are examples of other areas
that benefit from the results of a linear equation system. A system of linear equations is
a set of linear equations which, in turn, are degree 1 polynomials with real (or complex)
coefficients. When we come across a system of linear equations, the main objective is to
find a solution for it, which must simultaneously satisfy all linear equations. In this work,
we will present part of the systems theory of linear equations and will emphasize some of its
applications in different areas of knowledge. We will rely on several authors and especially
on: Boldrini (1986), Dante (2013) e Iezzi, G. Hazzan, S. (2004). The work also consists
of presenting some of the possible applications of systems of linear equations, aiming to
widen the reader’s knowledge about the study of linear equations. It is tried to solve
some situations problems that involve systems of linear equations. The research process
of the research consists of a bibliographical revision in Mathematical and Mathemati-
cal History books, articles, monographs and other scientific works that deal with the theme.
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