A system of linear equations consists of two or more linear equations with the same variables. It is an essential concept in mathematics as it helps us solve real-world problems that involve multiple unknowns and constraints. By representing these problems as systems of linear equations, we can find solutions that satisfy all the given conditions.

For example, let's consider a scenario where we want to determine the number of tickets sold for a movie. The revenue from ticket sales can be expressed as a linear combination of the number of adult tickets and the number of child tickets sold. Similarly, the total number of tickets sold can be represented as the sum of adult and child tickets. By setting up a system of linear equations, we can find the precise values for each variable and calculate the revenue or the number of tickets sold.

Another application of systems of linear equations is in mixing solutions. Suppose we have two different solutions, each with a given concentration, and we want to find out how much of each solution we need to mix to obtain a desired concentration. By setting up a system of equations based on the concentration and the amount of each solution used, we can determine the required quantities.

Systems of linear equations provide a powerful framework for solving complex problems in a systematic and organized manner. In the upcoming posts, we will explore different methods for solving these systems and delve into their applications in various fields.