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December 19th, 2007, 06:45 AM  #1 
Newbie Joined: May 2007 Posts: 18 Thanks: 0  3 variables, 2 equations
Hello! Is there any way to solve following set of equations: x + z = 2 y + 2z = 5 Thanks! 
December 19th, 2007, 06:58 AM  #2 
Senior Member Joined: Oct 2007 From: France Posts: 121 Thanks: 1 
For each z real, we have a solution (x,y), with: x=2z and y=52z 
December 19th, 2007, 07:40 AM  #3  
Newbie Joined: May 2007 Posts: 18 Thanks: 0  Quote:
 
December 19th, 2007, 07:57 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
There are an infinite number of solutions. For any possible z you might choose, you have (x, y, z) = (2  z, 5  2z, z). For example, the following are solutions: (2, 5, 0) (1, 3, 1) (0, 1, 2) 
December 19th, 2007, 08:39 AM  #5  
Newbie Joined: May 2007 Posts: 18 Thanks: 0  Quote:
 
December 19th, 2007, 09:26 AM  #6  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
 
December 21st, 2007, 12:02 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,973 Thanks: 2224 
Consider a geometrical interpretation: two planes intersecting in a line, rather than just one point.


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