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### 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/
```
Associated Topics:
Middle School Algebra

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