I am interested in starting another business. I need to have second
phone number for my new customers to call--so far not too tough. I
also need to be able to answer calls for both businesses on the same
phone  which means I need a way to identify the number the caller
called before I answer the call, so I can answer the phone
appropriately (for example, "Good morning, thank you for calling
company 1). A phone system that requires the user to choose the
correct company via telephony is not desireable. I have seen systems
like this before, but cannot remember where. The solution needs to
work with my existing phone system and not require additional
equipment. The solutions I am most interested are internet based.

This is very simple.

All you need are the two separate phone lines (I would recommend A
VOIP provider such as Lingo which would be the least expensive
option), and one phone that is a two-line phone. It would have a
blinking red light or a similar feature that would blink at either
"Line 1" or "Line 2."  You'd know at a glance if the customer's
calling for Business A or Business B.

It would be nice to have a link or two explaining how this solution is
internet based.