A system and a method automatically longitudinally guide a motor vehicle. The system is used to automatically brake the motor vehicle to a standstill on the basis of a detected infrastructure component which requires a braking of the motor vehicle to a standstill. The system includes a sensor unit which is designed to detect an infrastructure component that requires a braking of the motor vehicle to a standstill, a first determining unit which is designed to determine a standstill position on the basis of currently provided information of the sensor unit upon detecting the infrastructure component, a second determining unit which is designed to determine an adapted standstill position upon no longer detecting the infrastructure component on the basis of the determined standstill position when the infrastructure component was still detected, and a control unit which is designed to automatically initiate a braking to the standstill into the determined standstill position or the determined adapted standstill position.