In the present paper, for first time, a System of Neutrosophic Linear Equations (SNLE) is investigated based on the embedding approach. To this end, the (a,b,g)-cut is used for transformation of SNLE into a crisp linear system. Furthermore, the existence of a neutrosophic solution to n x n linear system is proved in details and a computational procedure for solving the SNLE is designed. Finally, numerical experiments are presented to show the reliability and efficiency of the method.