# Rates of substitution

### From Glossary

Arises when equations are split into dependent (or basic) variables and independent (or nonbasic) variables. In linear programming, we rewrite
as where is the vector of basic variables and is the vector of nonbasics. Then, the original equations are equivalent to
where
and
This implies that the *rate of substitution* between and is because it describes the marginal rate at which must change in response to a change in to maintain the equations with all other 's held fixed.