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Topic: Inconsistent equations?
Replies: 1   Last Post: May 25, 2013 2:17 PM

 James Waldby Posts: 472 Registered: 1/27/11
Re: Inconsistent equations?
Posted: May 25, 2013 2:17 PM

On Sat, 25 May 2013 09:14:04 -0700, Peter wrote:
> On Saturday, May 25, 2013 10:22:19 AM UTC-4, Peter wrote:
>> Hi! Please, this system of two equations seems to be inconsistent. Is it? How can I tell? m1 r1 ?1 = m2 r2 x and m1 r12 ?12 = m2 r2 x2. m1 and m2 cannot be equal, neither can be r1 and r2 . I would appreciate any additional information someone can give me. Thanks.
>
> The correct equations are:
> m1 r1 w1 = m2 r2 x
> and
> m1 r1^2 w1^2 = m2 r2^2 x^2.

On Sat, 25 May 2013 10:50:07 -0700, Peter wrote: ...
> No variable can be zero, and the ms and rs cannot be equal; so, there is no solution for x. Agree?

Given your added condition "No variable can be zero" it is easy
to properly prove the equations inconsistent. Note, for clarity
in following I write m, r, w instead of m1, r1, w1, and
n, s instead of m2, r2.

Given: m != n; r != s; (1) mrw = nsx; (2) mrrww = nssxx, with
juxtaposition denoting multiplication; (3) all of m, r, w, n, s,
x are nonzero.

From (1) (and supposing mrrww = mrwrw, etc), mrrww = nsxrw. Then
by (2), mrrww = nsxrw = nssxx = nsxsx. We suppose (3) then
implies rw = sx. So mrw = nsx = nrw, hence m = n, contradicting (3).

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