Final answer:
Elizabeth visits Derbyshire with the Gardiners for a change of scenery and agrees to visit Pemberley out of curiosity about the estate, not because she hopes to see Darcy.
Step-by-step explanation:
Elizabeth goes to Derbyshire with the Gardiners because she is invited by them, and it presents a chance for a change of scenery. She agrees to visit Pemberley, Darcy's estate, because despite some initial reluctance—and not because she hopes to see Darcy—she is curious about the place.
It is one of the most beautiful estates and she is assured Darcy is not present, so the visit could occur without the awkwardness of encountering him. This decision illustrates Elizabeth’s growing maturity and her ability to separate her personal feelings from social expectations.