Final answer:
The administration of a second solution through a previously established IV line is known as a Secondary infusion. For home administration of an antimicrobial to treat a systemic infection, the oral or parenteral routes are typically the most appropriate and convenient.
Step-by-step explanation:
The name of the administration of a second solution through a site of an already established primary line is b) Secondary infusion. This method involves connecting a secondary set of intravenous (IV) tubing into the primary line for the administration of medications or solutions. This allows for the medication to be delivered at a controlled rate, using the same IV access already established.
Regarding the appropriate and convenient route for home administration of an antimicrobial to treat a systemic infection, the options are A. oral, B. intravenous, C. topical, and D. parenteral. The most suitable routes for home administration would typically be A. oral and D. parenteral (which can include subcutaneous, intramuscular, and intravenous under certain conditions). Oral administration is often preferred for its ease of use and convenience, whereas parenteral methods are chosen when the oral route is not suitable or when a more rapid or targeted effect is necessary.