[R] Solve equations

[Moshe Olshansky]

Hi Sebastian,

Your equations can be easily solved - no programming
is required!
Let's number you equations:

(1) 0.007= 2VZ
(2) 0.03= W(Y+Z)
(3) 0.034= X(y+Z)
(4) 0.013 = (X+W)Y +(X-W)Z
(5) X = W+V

Substitute (5) into (3) and then divide (2) by (3) to
get

(W+V)/W = 0.034/0.03 
so that 
(6) V = (2/15)*W
(7) X = V+W = (17/15)*W

Substitute (7) into (3) and (4) to get:
(3') (17/15)*(WY + WZ) = 0.034
(4') (32/15)WY + (2/15)WZ = 0.013

Solving (3') and (4') for two new unknowns WY and WZ
yields

(8) WY = 0.0045
(9) WZ = 0.0255

So that 

(10) Z = (17/3)*Y

Substitute (10) into (1) to get
2*Y*(17/3)*Y = 0.07

So (since Y > 0), Y = sqrt(0.21/34) = 0.07859052
>From (10), Z = (17/3)*Y = 0.4453463
>From (8), W = 0.0045/Y = 0.05725881
>From (6), V = (2/15)*W = 0.007634508
Finally, X = V + W = 0.06489332

So there is a unique solution (which luckily satisfies
your constraints!).

Regards,

Moshe.


--- sebastien puechmaille
<sebastien.puechmaille at ucd.ie> wrote:

> Hello,
> 
>  I have a system of five equations to solve with
> five 'unknows'(V, W, X,
> Y and Z) and  constraints. The equations are:
> 0.007= 2VZ
> 0.03= W(Y+Z)
> 0.034= X(y+Z)
> 0.013 = (X+W)Y +(X-W)Z
> X = W+V
> Constraints:
> 0<V<W<X
> 0<Y<Z<1
> 
> Does anyone know a R-package to solve this system?
> 
>  Thanks,
> 
> E-mail: sebastien.puechmaille at ucd.ie
> 
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