Decimal problem using solve

[Albert Chan]

(08-26-2018 02:57 AM)vterez Wrote:  (Brazilian here, sorry if my English is bad)
I was trying to use the solve function to do my homework and I noticed something really weird:
I was solving this equation
70/(23000+z)=x*177.35+(1-x)*1.133
(23000+z)*(x*2571.11+(1-x)*696.21)=23000*104.91+z*2779.65
on my calculator and for some reason I received {} as my answer.

If it were homework, I think it meant not using SOLVE, calculator only for number crunching.
You really should do y = 1/(23000+z), and simplified it by hand:

70*y = x*177.35+(1-x)*1.133
(x*2571.11+(1-x)*696.21) = (2779.65*(23000+z) + 23000*(104.91-2779.65)) / (23000+z) = 2779.65 - 61519020*y

Above simplified to linear equations:
70*y = 1.133 + 176.217*x
61519020*y = 2083.44 - 1874.9*x

Cancel the y's --> x ~ -0.00641604 --> z ~ 6358.11

Regarding the {} answer, I believe SOLVER assumed decimals as float, to speed up calculation.
Slight rounding error cause above into nonlinear equations.