A **system of linear equations** or a
**linear
system** is a collection of *linear
equations*

in the same variables, typically x_{1},
x_{2},
. . . , x_{n}.

An example of a system of two linear equations in three variables is

x_{1}
+ 2x_{2} - x_{3} = 4

2x_{1} -
4x_{2}
= 5