Two Businesses Under One LLC?

I do not know if this is a legitimate question or not. I feel so ignorant when it comes to this stuff, and I hope my question makes sense.

I am a full time teacher and a couple of years ago I formed an LLC and obtained a Federal EIN to teach a couple of classes on the side for some extra money. I have no plan to grow into something major - I just enjoy teaching and needed some extra money to provide for the family.

I also do web design, which has been mostly for non-profit organizations. But now I am starting to get paid for designing some websites for a couple of companies. I see this as more of a hobby that I get paid for as well.

My question is can I run my web design company under the same teaching LLC and Federal EIN, or do I need to form a separate LLC and obtain a second federal EIN? I am willing to do this, but the price for the LLC just seems like a lot right now when I am so small.

If I am not allowed to run the web design under my teaching LLC, then do I need an LLC and Federal EIN at all for the web design? Can I just file taxes as just making some money on the side through a schedule C?

Thanks for your time and help in advance!