 The algorithm is named after Joseph Fourier and Theodore Motzkin who independently discovered the method in 1827 and in 1936, respectively.The elimination of a set of variables, say "V", from a system of relations (here linear inequalities) refers to the creation of another system of the same sort, but without the variables in "V", such that both systems have the same solutions over the remaining variables.If all variables are eliminated from a system of linear inequalities, then one obtains a system of constant inequalities.