Final answer:
Chlorophyll b is the component not used by both plants and cyanobacteria to carry out photosynthesis, as cyanobacteria use phycobilins instead.
Step-by-step explanation:
The component not used by both plants and cyanobacteria to carry out photosynthesis is chlorophyll b. Plants and algae have different types of chlorophylls, including chlorophyll a and b. However, cyanobacteria use different accessory pigments called phycobilins instead of chlorophyll b. Although both organisms use chlorophyll a and carotenoids for photosynthesis, the presence of chlorophyll b is unique to plants and some algae, and not found in cyanobacteria.