Final answer:
The neural system associated with emotions and drives located below the cerebral hemispheres is the Limbic system, which includes the amygdala and cingulate gyrus.
Step-by-step explanation:
The neural system located below the cerebral hemispheres and associated with emotions and drives is the Limbic system. This system includes several important structures such as the hippocampus, amygdala, thalamus, and cingulate gyrus, which work together to regulate emotions, behaviors related to fear and motivation, and memory formation. The amygdala, for instance, is crucial for experiencing fear and recognizing fearful faces, while the cingulate gyrus helps to manage emotional reactions and pain.