I agree with your answer to part b, although you don't need to solve x and y (in fact, their solutions would depend on a).
As for part a), the system of linear equations has no solution when the lines are parallel (and so never cross). What do you know about parallel lines?
And for part c), the system of linear equations has infinitely many solutions when the two lines are in fact, the same. How can you use this piece of information to help you answer the question?