# Linear System

Pronunciation: /ˈlɪn.i.ər ˈsɪs.təm/ Explain

A linear system is a set of lines or linear objects that are all simultaneously true (true given the same circumstances). Together they define the solution(s) to the system.

Two methods commonly used to solve a linear system are:

• substitution and elimination; and
• Gauss-Jordan elimination.

### Substitution and Elimination

Substitution and elimination is a method for solving linear system. Given two or more linear equations, this method may be used to find the solution the linear system.

StepEquationsDescription
1Original equation
2Solve the first equation for y.
3Substitute 4-x for y in the second equation.
4Solve the second equation for x.
5Now substitute the value of x into the first equation.
6Solve for y. The solution to this linear system is y=1, x=3.
Example 1

### References

1. McAdams, David E.. All Math Words Dictionary, linear system. 2nd Classroom edition 20150108-4799968. pg 109. Life is a Story Problem LLC. January 8, 2015. Buy the book

### Cite this article as:

McAdams, David E. Linear System. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/l/linearsystem.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/31/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
11/27/2008: Changed equations to images. (McAdams, David E.)
8/23/2008: Added substitution and elimination example. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

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