Translation of "elimination" into Japanese

"Why me?" "Because, by process of elimination, there was no other choice."

「なんで私?」「消去法で仕方がなかったから。」

He thereby made sure that his enemies were properly disabled or eliminated .

敵 を 確実 に 排除 ・ 無力 化 さ せ た 。

His misspelling of that word eliminated him from the contest.

その語の綴りを間違って、彼はコンテストに失格した。