阅读理解

    A beautiful and very successful actress (女演员) was the star for a new musical show. Her home was in the countryside, but she did not want to go back there every night, so she bought an expensive house in the centre of the city, got some beautiful furniture and got a man to paint the rooms in new colours.

    It was very difficult to get tickets for her show, because everybody wanted to see it. So she decided to give the painter two of the best seats. She hoped that this would make him work better for her. He took the tickets without saying anything, and she heard no more about them until the end of the month, when she got the painter's bill (帐单). At the bottom of it were these words: “ Four hours watching Miss Hall sing and dance : 3 pounds,” with this note: “ After 5 p.m. I get 15 shillings (先令) an hour instead of 10 shillings.”

已知直线l₁：x+2ay﹣1=0，l₂：（3a+1）x﹣ay+1=0．

（1）当l₁∥l₂时，求a的值；

（2）当l₁⊥l₂时，求a的值．