  We explore new symmetries in two-component third-order Burgers' type systems
in (1+1)-dimension using Wang's O-scheme. We also find a master symmetry for a
(2+1)-dimensional Davey-Stewartson type system. These results shed light on the
behavior of these equations and help us understand their integrability
properties. Our approach offers a practical method for identifying symmetries,
contributing to the study of integrable systems in mathematics and physics.
