The and the are codependent. The respiratory system would not work without the muscular system.
The term respiration is characterized by gas exchange. Gas exchange first occurs at the alveoli in the lungs. Normal breathing in humans relies on what is called negative pressure inhalation. In order for air to be pulled into the lungs, the external intercostal muscles found between the ribs will contract, increasing the volume of the pleural space to increase. With an increase in volume, pressure in this space necessarily drops.
Because the pressure in the pleural space is less than the atmospheric pressure in the lungs, air from the outside will rush into the lungs. To exhale, the external intercostals are relaxed, volume of the pleural space decreases, its pressure increases, and air is forced out of the lungs.
In this way, the respiratory system is dependent upon the muscular system. However, the muscular system requires the oxygen that is brought in from the respiratory system to act as the final electron acceptor in oxidative phosphorylation. Without ##O_2##, the muscles would be unable to generate enough ATP to continue contracting and functioning properly in general.