Teacher2Teacher 
Q&A #6297 
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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 BC=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 = (1x1) (1x) = 2 Determinant B= 5 1 (Det B)  4 1 = 5x14x1= 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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