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Teachers' Lounge Discussion: Simultaneous equations

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From: Loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2001072318:50:24
Subject: Re: Simultaneous equations

Here is a simple example of Simultaneous equations which we will solve
by simple addition. 

A Bottle and a Cork cost a nickel.  The Bottle costs 4 cents more than
the Cork.  How much does each cost?

Let C=cork
Let B=bottle

B+C=5
B-C=4  (add these two equations together.
-------
2B =9  (Divide both sides by 2)
B=4.5 cents and C= 1/2 cent.

The thing about this problem, is that most people jump to conclusions
and give the answers as 4 and 1.  

If you know how to do determinants, you can solve this by Cramer's
rule.  Notice that the column vector | 5 | replaces the column vector 
                                     | 4 |
B and C when you are solving for B and C
              | 1  1 |
Determinant D=| 1 -1 |= (1x-1) -(1x) = -2

Determinant B=| 5  1|  (Det B)
              | 4 -1| = -5x1-4x1= -9 

Determinant C= | 1  5|
               | 1  4| = 1x4 -1x5=-1

B= Det B/Det D=-9/-2=4.5
C= Det C/Det D=-1/-2= .5

One other good way to solve this is by graphing which I will not do
now.  However, it is worthwhile for the student to graph these.  The
Coordinates of the point where the two lines cross is the answer.     




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