Speaking literally, there is only a single question:
- "Aren't you supposed to be there at 7?"
Also speaking literally, there is a single answering statement (although several different such statements are possible):
- "Yes, I am supposed to be there at 7."
- "No, I'm not supposed to be there at 7."
But in context, the second statement after the question can be taken as an implied, conditional question:
- Aren't you supposed to be there at 7? [If you are, I think] you don't have time [, do you?]
As such, the person answering could choose to provide a two-part answer:
- "Yes, I am supposed to be there at 7, and I think I'll make it."
- "Yes, I am supposed to be there at 7, but I think you're right that I won't make it."
- "No, I'm not supposed to be there at 7, so it doesn't matter if there isn't time to get there."
- "No, I'm not supposed to be there at 7, but I think I could make it anyway even if I were supposed to be there."
The following short answer could be seen as ambiguous:
- "No, I can make it on time."
In theory, it could be interpreted as a short version of the two-part answer expressed in 4: "No, I'm not supposed to be there at 7, but I could make it anyway even if I were supposed to be there."
However, idiomatically, it's not normally interpreted in such a literal sense. Instead, it's mostly understood that what is actually being answered is the implied, conditional question—and that the affirmative response to the actual first question is simply assumed.
In other words, it's meaning is commonly understood to be that of the two-part answer expressed in 1: "Yes, I am supposed to be there at 7, and [no, I don't think I don't have time, but] I think I'll make it."
However, there are no strict rules here. It depends on how the question has been interpreted as well as how the answer has been interpreted. Further, what sounds natural to one person in terms of an exchange might not sound as natural to another person. People differ between both their level of formality and their level of literalism.
To make this even clearer, consider this extreme example exchange:
- "Aren't you supposed to be there at 7? You don't have have time."
- "Yes."
- "No."
Rather than using any of the previously mentioned ways of answering, this simply provides a single-word answer.
This makes it even more ambiguous what is being answered, or, therefore, what the answer is.
The more something is not explicitly asked or answered, the greater the chance there is of it being confusing or misunderstood.