mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, a set of simultaneous equations, also known as a system of equations or an equation system, is a

finite set In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example, is a finite set with five elements. Th ...

equation In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for ...

s for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a: *

System of linear equations In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variable (math), variables. For example, : \begin 3x+2y-z=1\\ 2x-2y+4z=-2\\ -x+\fracy-z=0 \end is a system of th ...

, *

System of nonlinear equations In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathe ...

, *

System of bilinear equations In mathematics, a system of bilinear equations is a special sort of system of polynomial equations, where each equation equates a bilinear form with a constant (possibly zero). More precisely, given two sets of variables represented as coordinate v ...

, *

System of polynomial equations A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations where the are polynomials in several variables, say , over some Field (mathematics), field . A ''solution'' of a polynomial system is a se ...

, * System of differential equations, or a * System of difference equations

See also