Constancy of the speed of Light is incompatible with Galilean Transformations, because they predict that speed of light varies depending on the Inertial Reference Frame

Firstly, from an Electromagnetics perspective can be derived from Maxwell’s Equations, assuming an Inertial Reference Frame

Secondly, Galilean Transformations can be modified to account for a constant in all frames of reference as follows, resulting in the Lorentz Transformations