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, no solution, or infinitely many solutions, depending on how the equations relate to each other. Understanding systems of equations is essential in fields like mathematics, engineering, and economics.