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