In a display system, a color gamut of the displayed images is extended by adding one or more primary colors lying outside a tristimulus color space triangle to a Red, Green, Blue (RGB) system, modulating light emitted by both light sources lying inside the tristimulus color space triangle and light sources lying outside the tristimulus color space triangle, and adding a non-tristimulus vertex to construct an extended-gamut polygon. The display system adds one or more primary colors to the RGB system, which lie outside the tristimulus color space triangle but within a CIE (International Commission on Illumination) color space.