Linear systems of slots in a rectangular waveguide with the partial dielectric filling, excited by the slowed down wave are considered. The dielectric layer is parallel to wide walls of a waveguide. It is shown that not resonant system of longitudinal slots in a waveguide with a dielectric layer is more wideband in comparison with that in a hollow waveguide. For not resonant system of transversal slots possibility of scanning without interference maxima occurrence is shown. For resonant system of transversal slots possibility of one beam pattern formation is shown at almost full matching at the entrance.