In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables. For example,

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.