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The program for solving constrained equations using the Lagrange multipliers method, as provided by the teacher, contains detailed annotations that explain the logic and steps of the method. The annotations not only provide a clear understanding of the code but also offer valuable insights into the mathematical principles underlying the Lagrange multipliers method. For example, the annotations explain how the method generalizes the process of finding extrema of a function subject to constraints and how it involves solving a system of equations that incorporates the constraints into the Lagrangian function. Overall, the annotations demonstrate the teacher's mastery of the Lagrange multipliers method and their ability to convey complex mathematical concepts in a clear and concise manner.