For instance, say that you have the equation

y = (x-7)^2 + 3*(x-7) + 5

and (for no particular reason … but doesn’t that describe a lot of your math exercises, anyway 🙂 ?) you have figured out that x-7 = z. You can now put z in place of all those nasty x-7 terms, and get the simpler equation

y = z^2 + 3z + 5.

The substitution *method* says that you solve a problem by taking all of your information (such as two equations in two variables), and using that to isolate one variable. Then you use the implied substitution somewhere that it forms an equation with one variable fewer.

For instance, given

2(x+3) = 4y-6

x+y = 12

You start with the larger equation on top, and whittle that to

x+3 = 2y-3

x = 2y-6

Aha! We now have a expression for x. We now return to the other equation

x + y = 12

and substitute 2y-6 for each x, giving

(2y-6) + y = 12.

From here, it’s a short trip to 3y = 18, and y=6.

We now use substitution again, using 6 in place of y:

x+y = 12 turns into

x+6=12

Gee, x is 6, too … do you think they cheated? 🙂

Does that help? If not, feel free to message me.