Solve Using Elimination

Date: 01/24/2001 at 21:17:57
From: eva kandler
Subject: Algebra

Solve by using elimination, and check solutions:

   x + 6y = 20
   x + 2y = 12

Date: 01/26/2001 at 12:37:25
From: Doctor Alicia
Subject: Re: Algebra

Hi Eva,

To solve by elimination, think of your equations in this fashion: If I 
know that a = b, and that c = d, then it must be true that
  
   a - c = b - d

because I can subtract the same thing from both sides of an equation, 
and c and d are the same thing, because they're equal. 

So given something like: 

                   a      b
                   |      |

                 x + 6y = 20 

                 x + 2y = 12

                   |      |
                   c      d

I feel confident in writing: 

       a     -    c     =  b -  d      

    (x + 6y) - (x + 2y) = 20 - 12


So now what? Distribute the negative sign:

        x + 6y - x - 2y = 20 - 12

Combine like terms:  

                     4y = 8

Divide both sides by 4:

                      y = 2

Plug y = 2 back into either of the original equation and solve for x:

     [x + 6(2)] - [x + 2(2)] = 20

I hope this helps.  Write back if you have any further questions.
  
- Doctor Alicia, The Math Forum
  http://mathforum.org/dr.math/