My idea would be to check if any TM has empty language or not. Now if I can prove in some way that its not possible to find whether any TM has empty language or not then its also proved that this equivalence is undecidable. So I would encode a machine_A to halt on every TM A which accepts iff TM A terminates on input A.
And Therefore, deciding for all A whether machine_A accepts words or not, is the same as deciding for all Turing machines A whether it terminates on input A or not — and this is exactly the halting problem. Also since halting problem is undecidable, thus it is also undecidable.
