Editing Equation (section)

===Systems of linear equations===
[[File:九章算術.gif|thumb|[[The Nine Chapters on the Mathematical Art]] is an anonymous 2nd-century Chinese book proposing a method of resolution for linear equations.]]

A [[system of linear equations]] (or ''linear system'') is a collection of [[linear equation]]s involving one or more [[variable (math)|variables]].{{efn|The subject of this article is basic in mathematics, and is treated in a lot of textbooks. Among them, Lay 2005, Meyer 2001, and Strang 2005 contain the material of this article.}} For example,
:<math>\begin{alignat}{7}
3x &&\; + \;&& 2y             &&\; - \;&& z  &&\; = \;&& 1 & \\
2x &&\; - \;&& 2y             &&\; + \;&& 4z &&\; = \;&& -2 & \\
-x &&\; + \;&& \tfrac{1}{2} y &&\; - \;&& z  &&\; = \;&& 0 &
\end{alignat}</math>
is a system of three equations in the three variables {{math|''x'', ''y'', ''z''}}. A '''solution''' to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A [[Equation solving|solution]] to the system above is given by
:<math>\begin{alignat}{2}
x &\,=\,& 1 \\
y &\,=\,& -2 \\
z &\,=\,& -2
\end{alignat}</math>
since it makes all three equations valid. The word "''system''" indicates that the equations are to be considered collectively, rather than individually.

In mathematics, the theory of linear systems is a fundamental part of [[linear algebra]], a subject which is used in many parts of modern mathematics. Computational [[algorithm]]s for finding the solutions are an important part of [[numerical linear algebra]], and play a prominent role in [[physics]], [[engineering]], [[chemistry]], [[computer science]], and [[economics]]. A [[Nonlinear system|system of non-linear equations]] can often be [[approximation|approximated]] by a linear system (see [[linearization]]), a helpful technique when making a [[mathematical model]] or [[computer simulation]] of a relatively complex system.