Hamlet led a fencing match, his opponent's blade was poisoned. The wine was also poisoned, all this was planned by Claudius. Claudius was committed to putting an end to Hamlet, Claudius knew that Hamlet was his greatest threat. Killing Hamlet was the only way out for Claudius, one or both of them had to die. Hamlet foolishly fell into Claudius' trap, Hamlet's mother drank the wine in Hamlet's place. This was a tactical error made by Claudio, once he started his plan there was no turning back. Once Hamlet's mother died they knew poison had been used, Hamlet knew Claudius was responsible and Hamlet killed him with the poisoned blade. The same blade that ended Hamlet's life, this blade was able to kill them both. Claudio and his plan fell apart quickly, Claudio only cared about himself, that's why