So if you have (1) 2x + 3y = 8

(2) 3x – y = 6

Express (1) as 2x = 8 – 3y, or x = 4 – 3y/2

Now we use this expression of x in (2):

3(4 – 3y/2) – y = 6, or 12 – 9y/2 – y = 6 ==> 6 = 11y/2, or y = 12/11. Now use y = 12/11 in either (1) or (2) to solve for x.

In some word problems, we may need to translate the sentences into more than one equation. If we have two unknown variables then we would need at least two equations to solve the variable. In general, if we have n unknown variables then we would need at least n equations to solve the variable.

In the Substitution Method, we isolate one of the variables in one of the equations and substitute the results in the other equation. We usually try to choose the equation where the coefficient of a variable is 1 and isolate that variable. This is to avoid dealing with fractions whenever possible. If none of the variables has a coefficient of 1 then you may want to consider the Addition Method.

And, see: http://www.onlinemathlearning.com/algebra-lesson-substitution.html