It would be odd for both bulbs to die at once, but it is possible. I've gone through so many bulbs its insane in my 2001... The first few I had done under warranty they happened so quickly, but since they only replace the dead bulb and not the other, it would just alternate which was dead like a wig-wag... so I finally said F it and just fork over the $30 for a new pair of cheap ones when one dies on me, which is every year or two without fail. Battery's also been replaced twice on that vehicle whereas on my 1997 Mazda pickup I only just replaced the battery for the first time a few months ago and both headlight bulbs are original. Guess that's why the Elantra was as inexpensive as it was.
Check the fuse, then check the bulbs. Neither is hard or expensive to fix. Oh also don't try to change the bulbs in a parking lot... seems easy but that darn clip doesn't like to go back on for me and I always end up having to take the whole housing out which requires a ratchet with a longer extension than I typically have in the trunk, although it's still only a 5 minute job with the right tools.