A system of equations is a set of two or more equations that share common variables. The goal is to find the values of these variables that satisfy all equations in the system simultaneously. Systems can be classified as linear or nonlinear, depending on the nature of the equations involved. To solve a system of equations, various methods can be used, including graphing, substitution, and elimination. The solution can be a single point, indicating one unique solution, or it can be infinite or nonexistent, depending on the relationships between the equations. Systems of equations are widely used in fields like mathematics, engineering, and economics.