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#1 2006-12-29 05:04:16

mikau
Member
Registered: 2005-08-22
Posts: 1,504

four variables in three equations

Can this system of equations be solved?

1.  a1w + b1x = c
2.  a2x + b2y = c
3.  a3y + b3z = c

(note a1 and a2 are different variables)

ordinarily we need n equations for n variables. But here each equation only involves two variables. Seems like it might be possible.

Any ideas?


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#2 2006-12-29 06:57:22

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: four variables in three equations

It can be solved. But one of you variables(or maybe more) will be "floating" - that means, that it can be every element of some domain, and the other variables will depend of it.


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#3 2006-12-29 10:32:19

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: four variables in three equations

Hmm... and how can it be solved for a  "floating variable"?


A logarithm is just a misspelled algorithm.

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#4 2006-12-29 11:56:57

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: four variables in three equations

by floating, do you mean that one of the variables will be able to take any value within a certain domain, and the others depend upon what it is.

sorta like, you might have a = 10, and therefore b would be 6, and c would be 9, or if you set a = 12, you would have b = 3, and c = 12.

(random example) so that there isnt 1 single set of values that will satisfy the equations?


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#5 2006-12-30 03:53:45

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: four variables in three equations

luca-deltodesco wrote:

by floating, do you mean that one of the variables will be able to take any value within a certain domain, and the others depend upon what it is.

sorta like, you might have a = 10, and therefore b would be 6, and c would be 9, or if you set a = 12, you would have b = 3, and c = 12.

(random example) so that there isnt 1 single set of values that will satisfy the equations?

Exactly. In general.


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