There are two motives for Darcy to help the Bennets. One is that he is in love with Lizzy and wants to relieve her distress at Julia's elopement with Wickham. Another is that he believes he is partly to blame for the elopement because he had not exposed Wickham's nature, which he had failed to do out of personal pride.
It was later revealed that Mr. Darcy provided the funds for George Wickham to marry Lydia, in order to repair the damage Wickham had caused and ensure Lydia's reputation and the Bennet family's honor were preserved.
Elizabeth tells Darcy about Lydia and Wickham in order to seek his help in locating them and potentially preventing a scandal. She also hopes that Darcy, as someone who cares about her and her family, will be motivated to assist in resolving the situation.
If Lydia marries Wickham, then Elizabeth will be closely related to a man Darcy detests. If Lydia fails to marry Wickham, then Elizabeth will be a member of a disgraced family. Either way a connection between Darcy and Elizabeth is also a connection between Darcy and a scandal. Lizzy is already aware of the enormous differences between her situation and Darcy's. She is poor and he is rich. In England of the time, that was regarded as a reason for them not to be married, because marriage was a way to form alliances and increase wealth. Darcy has commented on this. Her family is not well bred by Darcy's standards, and Darcy has commented on this also. She has already turned down a marriage proposal by Darcy, and rather angrily. She regards the attraction Darcy has for her as probaby very weak to begin with. Lydia's elopement, in her view, is just a final straw.
Mr. Darcy gave George Wickham the money to marry Lydia in order to save the Bennet family's reputation and to ensure Lydia's well-being. Wickham had previously tried to elope with Lydia without intention of marrying her, which would have brought shame upon the family.
Lydia was supposed to keep Darcy's involvement in her wedding secret. Darcy had provided what was, in essence, Lydia's dowry, the money Wickham demanded to marry Lydia (though Lydia might have been unaware of the fact that Wickham would not have married her otherwise). This money was was used to buy Wickham an army commission and pay his debts. Darcy paid for the wedding, and attended it as best man.
In Jane Austen's novel "Pride and Prejudice," it is Mr. Darcy who finds Lydia Bennet and George Wickham after they elope. Mr. Darcy then arranges for their marriage to avoid scandal and uphold Lydia's reputation.
The conflict was solved after the letter which Darcy wrote to Elizabeth. It was only after reading the letter that Elizabeth started to realise her misjudgement and started to reflect and changed her opinion of Darcy. Elizabeth was able to forget about her initial prejudice of Darcy and see things from another point of view. Darcy's willingness to ditch his pride also contributed to the improvement in their relationship.
Mr. Darcy plays a significant role in resolving the Lydia-Wickham scandal in "Pride and Prejudice" by providing financial assistance to help facilitate their marriage. By doing so, he prevents the potential ruin of the Bennet family's reputation and secures Lydia's future. Darcy's intervention highlights his growth in character and his willingness to act out of compassion and responsibility towards those he cares about.
Lydia is...family is...Lydia and family are...
Darcy payed the fee that Wickham asked for in exchange for marrying Lydia.He did not tell Elizabeth that he had done so, and did it purely for Elizabeth despite what Wickham had done to his sister (georgiana).
I would not say she was a foil to these young women. Georgiana provides Darcy with a way of reasoning dispassionately about Lydia's elopement. The fact that Georgiana had nearly eloped with Wickham made it possible for Darcy to see that Lydia's eloping was something that could just as easily have happened in his own family. Also, the fact that Georgiana had nearly run off with Wickham made him feel guilty about failing to warn the Bennets.
Mr. Darcy played a leading role in the search for Lydia and Wickham, as he was the one who ultimately found them and arranged for them to be married.