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May 31st, 2017, 09:09 AM  #1 
Banned Camp Joined: Aug 2011 Posts: 534 Thanks: 2  Simultaneous equations.
Can there be more than two simultaneous equations to be solved? If yes, How many ? If Simultaneous equations > 2, How they can be simplified? If No,Why Simultaneous equations cannot be greater than 2? Thanks & Regards, Prashant S Akerkar Last edited by prashantakerkar; May 31st, 2017 at 09:11 AM. 
May 31st, 2017, 09:44 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,494 Thanks: 1369 
Enough is enough. Go away. 
May 31st, 2017, 09:53 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,805 Thanks: 2150  
May 31st, 2017, 09:58 AM  #4  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
 
May 31st, 2017, 10:01 AM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
You can have any number of simultaneous equations. A few points: if you have fewer equation than you do unknown terms, you cannot solve for specific values of those terms. For example, the single equation x+ y= 2 has an infinite number "solutions", pairs of (x, y) that satisfy the equation: take any number for x and then y= 2 x gives an (x, y) solution. The two equation x+ y+ z= 4, 2x+ y z= 0 where there are two equations and three unknown terms have an infinite number of solutions.. If you subtract the first equation from the second, you get x+ 2z= 4. If z is any value at all, then x= 4 2z and y= 4 x z= 4+4z z= 4+ 3z give (x, y, z) that satisfies the equation. The three equations x+ y+ z+ u= 0, 3x y+ z= 1, y z u= 0, with four unknown terms have an infinite number of solutions. On the other hand, if you have more equations than unknown terms, you might have no solution at all. For example, the three equations x+ y= 2, x 3y= 2, 2x+ y= 5 has no solution. The only numbers that satisfy x+ y= 2 and x 3y= 2 are x= 1, y= 1 but they don't satisfy the last equation: 2(1)+ 1= 3 not 5. If you have the same number of equations and unknown terms, say three equations and three unknown terms, there will be, generally, a unique solution. You do have to be careful that the equations are "independent". For example, the three equations x+ y+ z= 4, x y+ z= 1, and 2x+ 2z= 5 are not independent the last equation is just the sum of the first two. Any (x, y, z) that satisfy the first two (and, since that is two equations in three unknowns, there are an infinite number of solutions) will necessarily satisfy the third. 
May 31st, 2017, 10:05 AM  #6 
Senior Member Joined: May 2008 Posts: 301 Thanks: 81 
Beer soaked fake gratitude follows. Solved. Thank you for those serious thoughtprovoking, intellectually invigorating questions. 
May 31st, 2017, 11:13 AM  #7 
Banned Camp Joined: Aug 2011 Posts: 534 Thanks: 2 
Thank you. As you mentioned,there can be any finite number of Simultaneous equations, Can we also have any number of Simultaneous equations having complex numbers to be solved? Thanks & Regards, Prashant S Akerkar 
May 31st, 2017, 11:28 AM  #8 
Senior Member Joined: Aug 2012 Posts: 2,342 Thanks: 731  
May 31st, 2017, 11:35 AM  #9 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  It is and so it was answered several times, but the ratio of legitimate questions to total questions remains close to zero. Moreover, and this is the real point, his legitimate questions are better answered by his doing a bit of research and learning something in context. 
May 31st, 2017, 11:45 AM  #10 
Senior Member Joined: May 2008 Posts: 301 Thanks: 81 
Beer soaked fake gratitude follows. Thank you for those serious thoughtprovoking, intellectually invigorating follow up questions. 

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