What are the ethical implications of lying to get into a course? I attend a small liberal arts college in the US. Through the cross-registration program, we are permitted to take classes at a large state university at no extra cost to us. However, we are only allowed to enroll in one course at a time; the system will not allow us to take two during the same semester. 

Next semester, I am interested in taking two courses at the university. The will both be very small; certainly under 15 students each. Both professors have told me I cannot attend their class without being officially enrolled (I asked both individually). I have been considering attending both classes and asking both professors to fill out the cross-registration form that would allow me to enroll in their class, but only turning in one professor's form. From my previous experience at this university, the registration takes 4-6 weeks to come through, but professors, of course, let you attend class before that happens, so they may forget about awaiting the registration during that time. Even if they ended up finding out that I never turned it in, I would still have received a month of instruction before that happens, which I find valuable. 

I am curious about the ethical concerns about this from the standpoint of the professors. Obviously by being there I am giving them more work, but they are not paid according to the number of students attending their classes. On the other hand, I know that class enrollment is really important to directors of departments and higher-ups in the university, so they are doing the work of teaching me without getting the benefit of one more student in their enrollment numbers. And from a personal standpoint, I would feel absolutely terrible about developing a good relationship with a professor and having them find out I lied to them.

I am not asking to be told what to do (it's probably not a very good idea), I would just like to know if there are any other concerns with lying to get into this course that I am not considering.

edit/update: Wow, I was not expecting to get so many responses. I'm not going to respond to comments and answers individually but I appreciate all your feedback, even though a few of you are a bit rude. I definitely will not be attempting to take both courses. Unfortunately, the program doesn't allow audits, so I am going to choose one of the two courses and stick with it. Thanks again for sharing all of your perspectives.
If I found out I was intentionally deceived by a student after telling them they could not take my class, I would alert my dean (I would go beyond the department chair) that said student was violating the rules and spirit of the exchange program. At a minimum I would expect that student to no longer be able to take advantage of the exchange and have their grade withheld from the other class. I would hope the home university would also punish this student for academic misconduct.