So I have these two equations:

x^3 + by + c = 0

y^3 + bx + d = 0

where x and y are functions of b, and c and d are constants. The task is to show that y = -x when d = -c. Which should be simple enough,

y^3 + bx + d = 0

y^3 + bx - c = 0

y^3 + bx - c = x^3 + by + c

-y^3 - bx = x^3 + by

but to me it looks like there's no way to go further than this, or am I missing something? Thanks! =))