Is it possible to play New Leaf on multiple systems with a cartridge?

Solution 1:

Yes. It is possible for you both to play on one game card. However, the game saves to the cartridge, not the actual system itself. Therefore, you will have to share the same town. The only problem is that one of you will be the mayor, and the other will be a resident in the town. It doesnt affect much except your ability to create public works projects and create ordinances, really something the two of you can discuss in person and work out in the real world. Other than that, the game will be almost identical, except for some of the villagers not calling you the mayor.

Here's a discussion on the official Nintendo forums about using the same cartridge on multiple 3DS systems.

Have fun!