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Re: Solve[] for equations?

Are you sure there is a solution? I tried a system of two equations and here
the solution doesn't exist:

eq1 = Rac == R1*(R2/(R1 + R2));
eq2 = Rad == R2*(R1/(R1 + R2));
Timing[Solve[{eq1, eq2}, {R1, R2}]]
{0.*Second, {}}

Mathematica gives the right answer: there is no solution, as can be verified
by hand. Either R1+R2 = 0, which leads to an indetermination in both
equations, or Rac = Rad, which makes the system trivial. However, the
three-equation system does have a solution:

eq1 = Rac == R1*((R2 + R3)/(R1 + R2 + R3));
eq2 = Rad == R2*((R1 + R3)/(R1 + R2 + R3));
eq3 = Rbc == R3*((R1 + R2)/(R1 + R2 + R3));
Timing[Solve[{eq1, eq2, eq3}, {R1, R2, R3}]]
{0.17 *Second,
  {{R1 -> (Rac^2 - 2*Rac*Rad + Rad^2 - 2*Rac*Rbc -
       2*Rad*Rbc + Rbc^2)/(2*(Rac - Rad - Rbc)),
    R2 -> (-Rac^2 + 2*Rac*Rad - Rad^2 + 2*Rac*Rbc +
       2*Rad*Rbc - Rbc^2)/(2*(Rac - Rad + Rbc)),
    R3 -> (-Rac^2 + 2*Rac*Rad - Rad^2 + 2*Rac*Rbc +
       2*Rad*Rbc - Rbc^2)/(2*(Rac + Rad - Rbc))}}}

You may verify the solution by direct substitution of these rules in the
equations. Then, there is no solution for the 2-equation case, but there is
a solution for the 3-equation case. I tried to set up a similar system with
five equations, but it was taking too long to solve before I quit (over 30
minutes). I only wish to point out that there may actually not be a solution
for the 4 equations (and, by the way, 4 equations in 4 unknowns doesn't mean
anything unless they are linear equations).

Tomas Garza
Mexico City

----- Original Message -----
From: "Doug VanGoethem" <djvango at>
To: mathgroup at
Subject: [mg31941] [mg31928] Solve[] for equations?

> I have a system of equations
> eq1 = Rac == R1(R2+R3+R4)/(R1+R2+R3+R4)
> eq2 = Rad == R2(R1+R3+R4)/(R1+R2+R3+R4)
> eq3 = Rbc == R3(R1+R2+R4)/(R1+R2+R3+R4)
> eq4 = Rbd == R4(R1+R2+R3)/(R1+R2+R3+R4)
> I'd like to get R1, R2, R3, and R4 in terms of Rac, Rad, Rbc, and Rbd.
> equations, four unknowns -- it seems simple in concept so I figured
> could do it easily.  I thought that something along the lines of:
> Solve[{eqs},{R1, R2, R3, R4}] or
> Solve[{eqs}, R1, {R2, R3, R4}]
> would have worked, but these give {}.  They only permutation of commands
> that seemed to do anything was something like
> Solve[eq1, R1]
> but one can do that easily by hand so what's the point.
> Is there some other command I should be using besides Solve?   Is there
> mathematical reason that I don't recognize as to why this won't work?   I
> would appreciate any insights.
> Thanks in advance,
> Doug VanGoethem

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