Elimination is a technique used in the solution of simultaneous equations by which n equations in n variables are reduced to one solvable equation in one variable, the process being repeated until all the equations are solved for all the variables. The process may be performed by establishing the value if one variable in terms of another and substitution; or by the addition to or subtraction from one equation of another. Thus

 

    if x – 6 = y   (1)
    and 2x + 3 = y   (2)

 

we can substitute the value of y in equation (1) into equation (2) to give

 

    2x + 3 = x - 6
    and hence x = –9.

 

Substituting the value into equation (1) gives y = –15.