Pure exchange economy with two consumers and non differentiable utility functions
I would suggest that ask yourself the following questions (hopefully, this should help you figure out how to solve the problem) : 


If good $z \in (x,y)$ was free, what would be the demand for both agents?
Is the conjunction of these demands feasible given the endowments? (this should allow you to rule out one of the cases)
If the demands are feasible, which price(s) for the other good would support such demands? What could be the equilibrium(a) allocation(s)?


Notice that if good $z$ is free, one of the agents is not able to consume the other good, and she is therefore indifferent between consuming any quantity of good $z$.

Hope this helps.