# elimination

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 2*x* + 3 = *y* (2)

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

2*x* + 3 = *x* - 6

and hence *x* = –9.

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