System of Equations and the Substitution Method

Date: 06/07/98 at 21:54:10
From: Rachael Poindexter
Subject: System of equations: Substitution method

I have been flipping page after page in every single math book I own, 
and none of them tells how to do the Substitution method, yet they all 
talk about it. I was wondering if you could send some directions and 
perhaps an example. I appreciate any help you might be able to give 
me. Thanks!

--Rachael Poindexter

Date: 06/08/98 at 12:48:33
From: Doctor Gary
Subject: Re: System of equations: Substitution method

Suppose, for example, that I told you that Susan was two years younger 
than Greg, and asked you Susan's age. All you would know was that:

   s  =  g - 2

Now, if I told you that Greg was 18, you could "substitute" 18 for g 
in the first equation, and learn that Susan was 16.

"Substitution" is based on the principle that, although we can't solve 
an equation with two unknowns, we can solve it if we can find a way to 
re-express the equation with only one unknown.

If you had the following two equations:

   3x + 2y  =  10
   2x -  y  =   4

all you would have to do is use of the equations to express one of the 
variables in terms of the other. For example, you could use the second 
equation to express y as 2x - 4 (can you see the steps you'd take to 
get that result?). Now you can "substitute" (2x - 4) for y in the 
first equation:

   3x + 2(2x - 4)  =  10
   3x + 4x - 8     =  10
   7x              =  18
    x              =  18/7

If x is 18/7, then 2x is 36/7, so y must be 8/7 for the second 
equation to be true.  

Be sure to "test" your answers by trying them out in the 
other equation:

   3(18/7) + 2(8/7) = (54 + 16)/7 = 70/7 = 10    

-Doctor Gary,  The Math Forum
Check out or web site! http://mathforum.org/dr.math/