My Math Forum 3 variables, 2 equations

 Algebra Pre-Algebra and Basic Algebra Math Forum

 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=2-z and y=5-2z
December 19th, 2007, 07:40 AM   #3
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 Originally Posted by Richard André-Jeannin For each z real, we have a solution (x,y), with: x=2-z and y=5-2z
Thanks, but I meant if there's a numeric solution? I would think I have too little information to find values for x, y and z, based on this information alone.

 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
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 Originally Posted by CRGreathouse 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)
Can you calculate those sets?

December 19th, 2007, 09:26 AM   #6
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 Originally Posted by morning_mood Can you calculate those sets?
Richard and I already have, but it's not possible to list them here. They're infinite in size. Would you like a gigabyte of solutions in plain text? How about a trillion gigabytes? That's not even scratching the surface.

 December 21st, 2007, 12:02 AM #7 Global Moderator   Joined: Dec 2006 Posts: 20,633 Thanks: 2080 Consider a geometrical interpretation: two planes intersecting in a line, rather than just one point.

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