You can play the multiplayer version of Nintendo DS games even if only one Nintendo system has the game using the "Download Play" option. For this to work, both systems must be in wireless range which is typically 20 feet or so.

On the Nintendo DS system that has the game cartridge, start the game.

On the other system choose "DS Download Play" from the main screen. Once you do this, it will scan for other systems and games. Once the game/system for your friend show up, select it and accept the confirmation. This will then download the game to your system.

You can then both choose the multiplayer option for the game and you'll be able to play against/with each other, even with only one game cartridge.