Which system provides MLG brake pressure when the hydraulic system No. 3 pump is not operating?

The system that provides main landing gear (MLG) brake pressure when the hydraulic system No. 3 pump is not operating is the Backup Brake System. This system is designed to maintain brake functionality in the event of a primary hydraulic failure, ensuring safety and operational capability.

The Backup Brake System typically utilizes a separate reservoir or a different hydraulic source to allow for braking even when the main hydraulic systems are compromised. This redundancy is critical for aircraft operations, as it enhances safety by providing an alternative means to apply brakes when needed.

The other systems, such as the Primary and Emergency Brake Systems, either rely on the normal hydraulic pressure supplied by the pumps or are specifically designed for different emergency scenarios, which do not typically cover the loss of hydraulic system No. 3. Therefore, the Backup Brake System is the correct answer as it specifically addresses situations where the primary hydraulic pressure is unavailable.