Plz help me solve for x and y

Question

x^3+y^3=1
x^4+y^4=1
help???

Answer 1

clearly, x and y are non-negative. For, if x^3+y^3=1, then if x<0, y>1, and then x^4+y^4>1.

Other than (0,1) and (1,0) I cannot think of any real solutions.