A method of solving algebraic equations by replacing one variable with an equivalent quantity in terms of other variable(s) so that the total number of unknowns will be reduced by 1. For example, to solve the following simultaneous equations:x + y = 3 (1)

and

x - y = 1 (2)

we can first obtain x in terms of y using equation (1):

x = 3 - y (3)

Then, we substitute x with (3 - y) in equation (2):

(3 - y) - y = 1 (4)

3 - 2y = 1

3 - 1 = 2y

2 = 2y

y = 1

As shown, we reduce the number of variables in equation (2) from 2 to 1 using the substitution method. As a result, we obtain a new equation with only one variable. Therefore, we can solve for y. Next, we substitute y = 1 back to equation (1) to solve for x:

x + 1 = 3

x = 2