Prove Subset can't be coset with two different subgroups

[FanofAFan]

Prove that a subset S of a group G cannot be a right coset of two different subgroups of G.

I having a hard time proving this... but this is what I have so far;
Fix z in H_z and since z = ez where e is in H. Then assume z in H_y by the right coset equation then with x = z we see that H_z = H_y and if H_x intersection of H_y $$\neq$$ to the empty set... that as far as i got. Please help

 

[Greg Bernhardt]

please repost using the template