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From: Loyd <firstname.lastname@example.org> 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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