Lie symmetry and conserved quantity of a system of first-order differential equations

This paper focuses on studying the Lie symmetry and a conserved quantity ofa system of first-order differential equations. The determining equations ofthe Lie symmetry for a system of first-order differential equations, fromwhich a kind of conserved quantity is deduced, are presented. And theirgeneral conclusion is applied to a Hamilton system, a Birkhoff system and ageneralized Hamilton system. Two examples are given to illustratethe application of the results.