What is linear system?

A linear system is a set of two linear equations with two variables.   

For example, 2x + y = 5 and x – y = 5x 

These are linear equations with two variables and when considered together, they form a linear system.

Uses of linear systems

Linear systems are used in various fields, including mathematics, science, engineering, and economics. They are used to model real-world phenomena, such as the motion of objects, the behavior of circuits, and the interactions of markets.

Here are some examples of how linear systems are used in different fields:

1. Mathematics: Linear systems are used to solve a variety of mathematical problems, such as finding the roots of polynomials and finding the solutions to systems of equations.
2. Science: Linear systems are used to model physical phenomena, such as the motion of objects, the behavior of circuits, and the spread of diseases.
3. Engineering: Linear systems are used to design and analyze engineering systems, such as bridges, buildings, and airplanes.
4. Economics: Linear systems are used to model economic phenomena, such as supply and demand, and to make economic predictions.

Why study linear systems?

Studying linear systems is very beneficial for students interested in a career in the fields of engineering, computer science, economics, finance, and academic research, which can give them a significant advantage. 

Linear systems are a fundamental part of many other fields, such as statistics and operations research. So, even if the students are unsure of what they want to do as a career, studying linear systems can give them a broad foundation in mathematics and problem-solving skills that can be useful in many different fields.