I think this is an invalid problem.
It looks, in the diagram, as if angle ABC is a right angle, and also as if triangle BDC is isosceles; but neither of these can be assumed without being told (in words, or by a marking). So the diagram tells us nothing new that we could use to find x and y. So there is no valid answer for (b), and no unique answer for (c).
In particular, I get different answers if I assume either of the two possibilities I mentioned! So no solution completely fits the appearance of the diagram.
So I would answer (a), and then state that there is no second equation to write. Or, I would ask my teacher if I am expected to assume something from the picture.