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August 26th, 2011, 01:39 AM  #1 
Senior Member Joined: Aug 2011 Posts: 422 Thanks: 2  Simultaneous Equations
Referring to Definition of Simultaneous equations http://en.wikipedia.org/wiki/Simultaneous_equations For example, x+y=3 xy=5 The Above case has two variables x & y > 2 Answer: x=4 y=1 Question 1: Since Simultaneous equations involves multiple variables, what are there any rules for creating Simultaneous equations? i.e Are these valid examples? 1. x+y+z=3 xyz=4 The above involves 3 variables, since there are three variables do we have to have 3 Simultaneous equations to calculate value of x,y & z? i.e say one of equation to be added say 2x+2y5z=1 2. a+b+c+d=4 2ab+c2d=5 The above involves 4 variables, The above involves 3 variables, since there are four variables do we have to have 4 Simultaneous equations to calculate value of x,y & z? say 3a+2b+2cd=1 5a+3b3c+3d=3 Question 2: Can I have both Upper and Lower case Letters in Simultaneous Equations? Are these valid examples? Example 1: x + X =4 x  X =6 Example 2: x + Y = 1 x  Y = 7 Question 3: Since there are 26 Upper case characters A.... Z and 26 Lowe case characters a ... z which gives us a count of Total 52 variables, can we construct Simultaneous equations as an example to compute all values of the 52 variables? So do we have to write 52 Simultaneous equations in this case? Thanks & Regards, Prashant S Akerkar 
August 26th, 2011, 04:33 AM  #2  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 5  Re: Simultaneous Equations Quote:
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About 20 years ago, the United States did a project to "justify" township lines on geodesic maps. If you have ever looked at a detailed geodesic map, you may have noticed that lines marking township boundaries often did not quite "match up" due to slight surveying errors (You can imagine the problems surveying land at the crest of the Rocky mountains!). Rather than go back and resurvey everything, the Department of the Interior solved several thousand equations in several thousand unknowns, using statistical methods to match everything up with minimum error. Quote:
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August 26th, 2011, 10:28 AM  #3 
Senior Member Joined: Aug 2011 Posts: 422 Thanks: 2  Re: Simultaneous Equations
Thank you. Thanks & Regards, Prashant S Akerkar 
August 29th, 2011, 02:17 AM  #4 
Senior Member Joined: Aug 2011 Posts: 422 Thanks: 2  Re: Simultaneous Equations
Thank you. Can we come to a conclusion and note down the laws of Simultaneous Equations? The Number of Simultaneous Equations is greater than or equal to the Number of computing finite unknown variables. OR The Number of Simultaneous Equations is directly proportional to the Number of computing finite unknown variables. As a example, if there are three variables to be computed in simultaneous equation/s, then we have to write three or more Simultaneous Equations. Would anyone like to make amendments in the Simultaneous Equations Laws? Thanks & Regards, Prashant S Akerkar 
August 29th, 2011, 02:31 AM  #5  
Senior Member Joined: Feb 2010 Posts: 600 Thanks: 87  Re: Simultaneous Equations Quote:
 
August 29th, 2011, 04:16 AM  #6 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Simultaneous Equations
Read this section of the wiki article http://en.wikipedia.org/wiki/System_of_ ... l_behavior Then read the whole article. Then read a book on Linear Algebra. 

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