section_path: Algebra/Systems of linear equations
section_name: Systems of linear equations
paragraph_text: Systems of linear equations
  
  A system of linear equations (or linear system) is a collection of linear equations involving one or more variables. For example,
  
  is a system of three equations in the three variables 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 solution to the system above is given by
  
  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 algorithms 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 system of non-linear equations can often be approximated by a linear system (see linearization), a helpful technique when making a mathematical model or computer simulation of a relatively complex system.