Given a+bY<=X and c+dX<=Y, can I find the necessary and sufficient condition of parameters a,b,c, and d such that the set (X,Y) is non-empty?

I am really confused about this simple math. I know if given by<=X and dx<=Y, then (X,Y) is non-empty iff b<=1/d. how come making the inequalities a little bit complicated cannot get the condition?

I feel like I'm running into a circle without a way out. And I really appreciate if someone can help me. Thank you so much.

Desparate Tref