A linear system is a collection of linear equations that share the same variables. Each equation represents a straight line when graphed on a coordinate plane. The solutions to a linear system are the points where these lines intersect, which can be one point, no points, or infinitely many points, depending on the relationships between the equations. Linear systems can be solved using various methods, including substitution, elimination, and graphing. These methods help find the values of the variables that satisfy all equations in the system simultaneously. Linear systems are widely used in fields such as engineering, economics, and science to model real-world situations.