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June 26th, 2017, 09:33 PM  #1 
Newbie Joined: Jun 2017 From: Wisconsin Posts: 15 Thanks: 0  Help with Solving a System of Equations with a Unique Solution
I'm a bit confused by the Echelon Method. The directions in my example say to solve a system of equations with a unique solution. From the reading I gather that a unique solution is one in which the line of two graphs intersect at one point. The two equations listed are: 3x + 10y = 115 11x + 4y = 95 The solution states: We first use transformation 3 to eliminate the xterm from the equation (2). We multiply equation (1) by 11 and add the results to 3 times equation (2) Transformation 3 says we replace any equation by a nonzero multiple of that equation plus a nonzero multiple of any equation. What exactly does that mean? The solution continues algebraically: 11(3x + 10y) = 11 * 115 > 33x + 110y = 1265 3(11x + 4y) = 3 * 95 > . 33x  12y = 285 __________________ 98y = 980 What just happened? I see the 33 and 33 cancel each other out and we get 33 in the first equation by 11*3 and 33 in the second equation by 3*11, but why did we have to multiply by 11 and 3 in the first place? In the second part of solving this problem the solution states that the first equation remains unchanged and the new system becomes: 3x + 10y = 115 98y = 980 Why did the first equation remain unchanged? Then it says to use transformation 2, which is "multiply both sides of an equation by any nonzero real number", to make the coefficient of the first term in each row equal to 1. Hence we must multiply equation 1 by 1/3 and equation 3 by 1/98. The confusion is in transformation 2 it doesn't say anything about making the coefficient 1, so how do we know this? It states it in my solution but not in the transformation. Am I missing something? 
June 26th, 2017, 10:01 PM  #2  
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
FYI, this thread should be in the Algebra forum, not Abstract Algebra. Quote:
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June 26th, 2017, 10:15 PM  #3 
Newbie Joined: Jun 2017 From: Wisconsin Posts: 15 Thanks: 0 
Thank you. How do I move my thread to algebra? My 
June 26th, 2017, 10:32 PM  #4 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  

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