A printing system is provided having a media width printhead, a plurality of ink containers fluidically interconnected with the printhead via a respective plurality of ink tubes, a plurality of gas vents fluidically interconnected with the printhead via a respective plurality of gas tubes, and a multi-channel valve arrangement for selectively moving a first pinch element into and out of pinching contact with the ink tubes so as to respectively block and allow fluid flow through the ink tubes and selectively moving a second pinch element into and out of pinching contact with the gas tubes so as to respectively block and allow fluid flow through the gas tubes.