System of Linear equations
A collection of two or more linear equations that have same set of variables is called a system of linear equations.
Introduction
The meaning of system is a set of connected things. In some cases, two or more linear equations have a connection and the relationship between them can be understood from their same set of variables.
Example
$x+3y-5 = 0$ and $7x-8y-6 = 0$ are two linear equations.
The two linear equations have a connection and it is they both have same set of variables $x$ and $y$. Therefore, a collection of such linear equations is called as system of linear equations and it is simply called as linear system.
When $x = 2$ and $y = 1$, the two linear equations are satisfied simultaneously.
- $2+3(1)-5 = 0$
- $7(2)-8(1)-6 = 0$
Therefore, the system of linear equations $x+3y-5 = 0$ and $7x-8y-6 = 0$ are called as simultaneous linear equations.
Methods of solving
The system of simultaneous linear equations can be solved in three different methods.