In
mathematics, a
system of linear equations (or
linear system) is a collection of
linear equations involving the same set of
variables. For example,
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=3201)
is a system of three equations in the three variables . 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.