The Method of Substitution

You have now seen how to solve a linear system by graphing or by elimination. There is yet another algebraic method known as substitution. This method involves solving a linear system by substituting for one variable from one equation into the other equation.

Remember that with each new method, you have more options for solving the linear system. You could, by all means, use elimination to solve every linear system you come across (or substitution), so it’s up to you to choose which method is best for which situation.

When it comes to deciding which method is best, it’s wiser to use substitution if you’re given an equation where a variable is already isolated for. Take for example:

x + 3y = 5    (1)

y = 4x – 1   (2)

Notice that in equation (2), y is already isolated. Therefore, you’re better-off using substitution since you won’t have to shift the terms around until they’re aligned as you would if you were eliminating.