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December 19th, 2007, 06:45 AM   #1
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3 variables, 2 equations

Hello!

Is there any way to solve following set of equations:

x + z = 2
y + 2z = 5

Thanks!
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December 19th, 2007, 06:58 AM   #2
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For each z real, we have a solution (x,y), with:
x=2-z
and
y=5-2z
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December 19th, 2007, 07:40 AM   #3
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Quote:
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.
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December 19th, 2007, 07:57 AM   #4
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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)
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December 19th, 2007, 08:39 AM   #5
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Quote:
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?
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December 19th, 2007, 09:26 AM   #6
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Quote:
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.
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December 21st, 2007, 12:02 AM   #7
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Consider a geometrical interpretation: two planes intersecting in a line, rather than just one point.
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