Pronunciation: /ˈlɪn.i.ər ˈsɪs.təm/ Explain
A linear system is a
of lines or
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.
|2||Solve the first equation for y.|
|3||Substitute 4-x for y in the second equation.|
|4||Solve the second equation for x.|
|5||Now substitute the value of x into the first equation.|
|6||Solve for y. The solution to this linear system is y=1, x=3.|
- 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.
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.)