Solving Pairs of Equations by Substitution

Date: 11/26/97 at 10:46:40
From: Lana 
Subject: Solving Pairs of equations by substitution

I am totally confused by this:

1.  x + 3y = - 5
   3x - 2y = 7

2. 3s - 4t = 5
    s + 7t = 10

3. 3m - n = 15
    m + n = 1

4. 2x - 3y = -4
  - x - 2y = 7


Please help me.
Thanks a lot.

Date: 12/18/97 at 10:50:37
From: Doctor Deanna
Subject: Re: Solving Pairs of equations by substitution

Hi there :)

Help is on the way. This confused me as well when I was first faced 
with it, but you'll see it's quite easy to understand and perhaps 
you'll find it a preferred method to solve equations, as I have.

Let's look at one of your problems and go through it step by step.

1.  x + 3y = - 5
   3x - 2y = 7

When you know what x is equal to, solving these equations is much 
easier. Substitution gives you a way to find x.

Take the first equation and solve for x.

x + 3y - 3y = -5 - 3y

          x = -5 - 3y

Now you have what you you need: what x is equal to. Next you need to 
insert it into the second equation. In other words, replace x with 
(-5 - 3y) just as you would if x were equal to a single number instead 
of another equation, like this:

3(-5 - 3y) - 2y = 7

Then solve for y doing the necessary computations.

You now will have an answer for y that doesn't involve any other 
variables. You're almost done - just one last step.

Take your answer for y and substitute it into either of the original 
equations (it doesn't matter which one) and solve for x again. This 
time you will get an answer for x that doesn't contain any variables.

Let me know if you need any further help on this but I think this 
should send you on your way.

-Doctor Deanna,  The Math Forum :)
 Check out our web site!  http://mathforum.org/dr.math/