The ability to solve quadratic equations is one of the main mathematical competencies of a modern high school student. But, unfortunately, quite often the solution of quadratic equations is reduced to a purely mechanical ability to insert the necessary numbers into the corresponding formula. Of course, modern mathematical education provides knowledge of the multiplication table, and the ability to find the roots of a quadratic equation. But in the contemporary world, which is permeated with computer technology, in the face of rapidly developing artificial intelligence, the development of computational skills fades into the background. In our opinion, the main thing in the study of mathematics is the ability to translate the phenomena of the surrounding world into the language of mathematics—mathematical modeling. This paper considers an algorithm for solving some systems of algebraic equations. Such systems are convenient for mathematical modeling, and the algorithm is based on the works of outstanding mathematicians of the past, such as Diophantus, Brahmagupta, and al-Khwarizmi.