Elimination

Noun

1. The act of eliminating, expelling or throwing off.
2. The act of excluding a losing contestant from a match, tournament, or other competition.

   "Everton require at least 3 goals in the second leg to avoid elimination from the FA Cup."

3. The act of voting off or throwing off a contestant in a reality television competition.
4. The act of discharging or excreting waste products or foreign substances through the various emunctories.
5. The act of causing a quantity to disappear from an equation; especially, in the operation of deducing from several equations containing several unknown quantities a less number of equations containing a less number of unknown quantities.