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 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. Each method aims to find the point(s) where the equations intersect, which represents the solution to the system. Systems of equations are widely used in fields such as mathematics, engineering, and economics.