Can I use cricut imagine cartridges with my original cricut?

Have you checked the manual/website on the model? Aside from thatr I think I see it listed briefly in thos FAQ

And couldn’t you just take the model number off the ones currently in it?

Supposedly you can. You would only get the cut portion of the cartridges, not the print aspect, so if the cartridge offers any outline cut options, you would be able to use those, if it only offers print such as background paper, then that wouldn’t work. I’ve heard that some stores are clearancing the earliest Imagine cartridges, and these are the ones that seem to have mostly print options. The most recent Imagine cartridges show objects and fonts on the packaging, and are priced higher, but they are supposed to work. There may be a firmware upgrade that you can get by connecting your cricut to the computer using a standard USB cord. This is necessary for the new Craft Room option available on the website, and it may be useful to make the Imagine cartridges work correctly.