substitution method
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:

symbol spacex + y = 3 (1)
and
symbol spacex - y = 1 (2)

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

symbol spacex = 3 - y (3)

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

symbol space(3 - y) - y = 1 (4)
symbol space3 - 2y = 1
symbol space3 - 1 = 2y
symbol space2 = 2y
symbol spacey = 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:

symbol spacex + 1 = 3
symbol spacex = 2

Related Term: elimination


 
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