# Substitution

## Origin

Middle English *substitucion*, from Middle French, from Late Latin *substitution*-, *substitutio*, from *substituere*

## Definitions

b: With reference to the principle in religious sacrifices of replacing one kind of victim by another or a bloody by an unbloody offering.

- 2: The designation of a person or series of persons to succeed as heir or heirs on the failure of a person or persons previously named.
- 3: a. The method of replacing one algebraic quantity by another of equal value but differently expressed.

- b. The operation of passing from the primitive arrangement of n letters to any other arrangement of the same letters.

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**this link**## Description

In mathematics, **substitution** of variables (also called *variable substitution* or *coordinate transformation*) refers to the substitution of certain variables with other variables. Though the study of how variable substitutions affect a certain problem can be interesting in itself, they are often used when solving mathematical or physical problems, as the correct substitution may greatly simplify a problem which is hard to solve in the original variables. Under certain conditions the solution to the original problem can be recovered by back-substitution (inverting the substitution).