Should I go with you to the supermarket? :)

Not really! The 'come with you to go at' is all wrong, I'm afraid. Remember that when we have movement, the preposition is 'to' - not 'at'. You could rephrase your sentence as 'Shall I come with you to the supermarket?'. This is OK, but might be more natural as 'Do you want me to come to the supermarket with you? This might imply that the person is to old, weak or afraid to go to the supermarket on their own. If you mean that you are offering to drive the person there, you could say, for example: 'Do you want a lift to the supermarket?' (GB English) 'Do you want me to take/drive you to the supermarket?' or you could just say: Shall we go to the supermarket, then? or So let's go to the supermarket. Just one last thought .... Your title is 'Is this a good question for the given answer?'. If 'We don't have any food for dinner tonight' is the given answer, surely the question should be something: 'Why do we have to go to the supermarket?'