MaplePrimes - answers and comments on Question, Simple Solution

The maple code for the

alex_01 — Sat, 27 Sep 2008 16:34:05 Z

sorry it should be

( 15,3440 * r_1 - 0.6329 + 5.7540 * r_2 ) /

( 21.0981 * r_1 - 3.1780 + 84.8348 *r_2 ) = 0.4573

The maple code for the equation is

0.4573 = (15.3440*r_1 - 0.6329+5.7540*r_2 ) / (21.0981*r_1 -3.1780 + 84.8348*r_2 );

The solution should be

r_1=0.175 and r_2=0.055

I can solve it the other way around

w_1:= (15.3440*r_1-.6329+5.7540*r_2 ) / ( 21.0981*r_1-3.1780+84.8348*r_2 );

r_1:=0.175: r_2:=0.055:

# which gives the output

w_1=0.4573

but not the other way..humm

momiji — Sat, 27 Sep 2008 18:08:01 Z

You only have one equation for your two variables, so there are an infinite number of solutions.

Calling solve on it directly, you get a description of them:

sol:={r_1 = -0.1440348680 + 5.800893388 r_2, r_2 = r_2}

Your particular solution is found by calling eval(sol, r_2=0.055);

alex_01 — Sat, 27 Sep 2008 18:33:01 Z

hummm,

so I guess it does not matter if we have two equations

w_1:=0.4573: w_2:=0.5427 # w_1+ w_2= 1

w_1 = (15.3440*r_1 - 0.6329+5.7540*r_2 ) / (21.0981*r_1 -3.1780 + 84.8348*r_2 );

w_2= (5.7540*r_1 - 2.5450 + 79.0808*r_2 ) / (21.0981*r_1 - 3.1780 + 84.8348*r_2):

We still cannot simultaniously solve for

r_1=0.175 and r_2=0.055 ??

momiji — Sun, 28 Sep 2008 00:43:20 Z

With two equations and two variables, you have a unique solution. In this case, solve finds and it is: {r_1 = 1., r_2 = 0.1972170132}