Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



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 UTC4, 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).
 jiw



