A method of solving linear simultaneous equations by reducing the number of variables by taking appropriate linear combinations of the equations. For example, when 3x + 2y = 7 (I) and 5x − 3y = −1 (II) then 3 × (I) + 2 × (II) ⇒ 19x = 19, so the variable y has been eliminated, allowing the variable x to be identified as 1, and then the substitution back into either of the original equations gives the corresponding value for y.