Yes you can, but with a few limitations in the case of the version 10 machine. We have that set up here where I use FileMaker Advanced 11 for development work, but have version 10 clients throughout the work place.
Both versions use exactly the same file format so there are no obvious glitches. The only case where you'll see a problem is if you have any features in your database that were newly introduced with the release of FileMaker 11. Filtered portals and charting are two of the most obvious "new with 11" features where you'll see this happen. If you access a layout with such features, the file shouldn't crash or anything, but the Filemaker 11 specific features to that layout won't work.