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#### Overview of this book

Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you’ll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges.
Preface
1. Fundamentals of Python
Free Chapter
2. Python's Main Tools for Statistics
3. Python's Statistical Toolbox
4. Functions and Algebra with Python
5. More Mathematics with Python
6. Matrices and Markov Chains with Python
7. Doing Basic Statistics with Python
8. Foundational Probability Concepts and Their Applications
9. Intermediate Statistics with Python
10. Foundational Calculus with Python
11. More Calculus with Python
12. Intermediate Calculus with Python

# Systems of Equations

An equation is an equality that we need to satisfy by solving for the values of a specific variable. In a system of equations, we have multiple equations involving multiple variables, and the goal is still the same: solving for the values of these variables so that each and every equation in the system is satisfied.

Overall, there is no limit to the number of equations a system can have. However, it can be rigorously proven that when the number of equations a system has is not equal to the number of its variables, the system has either infinitely many solutions or no solutions. In this section, we will only be considering the case where these two numbers match.

Additionally, we will consider two different types of systems of equations: systems of linear equations and those of non-linear equations. We will consider the methods of solving each of these two types of systems of equations, both by hand and by using Python. First, let's discuss the concept...