Final answer:
A repressible system uses negative feedback to decrease production of a substance when it is plentiful, exemplified by the trp operon. An inducible system also uses negative feedback but is activated by the presence of a substrate, such as lactose for the lac operon. Positive and negative feedback mechanisms are crucial for maintaining homeostasis and regulating biological processes.
Step-by-step explanation:
When matching the terms repressible system and inducible system with either positive or negative feedback, we need to consider how each system operates in response to the presence or absence of specific molecules. A repressible system, such as the trp operon in bacteria, utilizes a negative feedback mechanism. When the end product, in this case tryptophan, is in ample supply, it binds to the repressor, which then binds to the operator and prevents transcription, thereby reducing the production of additional tryptophan.
An inducible system, like the lac operon, operates through a form of negative feedback as well. However, it is 'induced' by the presence of a substance (lactose), which inactivates the repressor, allowing transcription to occur and enabling the metabolism of lactose. When lactose is no longer present, the repressor is not inactivated, and transcription is turned off.
Negative feedback mechanisms maintain homeostasis, while positive feedback mechanisms amplify or increase the activity of a process away from equilibrium. It's noteworthy that while the lac operon is considered to be under negative regulation because it turns off in the absence of lactose, the actual activation of transcription in the presence of lactose is a form of positive regulation.