Methods and systems for a transmission are provided herein. In one example, a hydraulic system includes a lubrication valve included in a lubricant line and designed to adjust a flow of lubricant to a multi-disc wet clutch. The hydraulic system further includes a clutch line coupled to a clutch control valve, where the clutch line is in fluidic communication with a hydraulic fluid to a clutch actuator of the multi-disc wet clutch and a passive adjustment device of the lubrication valve and where the passive adjustment device transitions the lubrication valve between a limited flow state and an open flow state based on a pressure of the hydraulic fluid in the clutch line.