In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables. For example, In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables. For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by