A fuel system includes a low-pressure fuel delivery unit; a high-pressure fuel delivery unit which has a drive region and a delivery region such that the drive region supplies fuel to the delivery region and such that the delivery region supplies fuel to a high-pressure fuel injector; a low-pressure fuel supply passage which supplies fuel from the low-pressure fuel delivery unit to the drive region of the high-pressure fuel delivery unit; a cooling passage which receives fuel from the drive region of the high-pressure fuel delivery unit; and a low-pressure fuel injector supply passage which is in direct fluid communication with the low-pressure fuel supply passage and which supplies fuel to a low-pressure fuel injector from the cooling passage.