A system for supplying a turbomachine with fluid, the supply system including a low-pressure pumping unit intended to increase the pressure of the fluid flowing toward a downstream circuit. The downstream circuit divides at an inlet node, situated between the low-pressure pumping unit and the high-pressure volumetric pump, into a circuit supplying an injection system and a variable geometries supply circuit. The circuit supplying the injection system includes a high-pressure volumetric pump. The variable geometries supply circuit is configured to convey the fluid toward variable geometry from the inlet node to an outlet node connecting the variable geometries supply circuit to the upstream circuit between two pumps of the low-pressure pumping unit.