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In mathematics, the theory of linear systems is a branch of [[linear algebra]], a subject which is fundamental to modern mathematics. Computational [[algorithm]]s for finding the solutions are an important part of [[numerical linear algebra]], and such methods play a prominent role in [[engineering]], [[physics]], [[chemistry]], [[computer science]], and [[economics]]. A 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.
 
== سادو ترين مثال==
==Elementary example==
The simplest kind of linear system involves two equations and two variables:
:<math>\begin{alignat}{5}