solving simultaneous Equations in R

Dear users of R,
I'm trying to solve the following 2 equations simultaneously in R for "x" and "y". I couldn't get through due to my limited knowledge of R.

3=1-[(x-1)!(2x-y-1)!/(2x-1)!(x-y-1)!] 

6={[(x-y-1)!/(x-1)!]-[3(2x-y-1)!/(2x-1)!]+[2(3x-y-1)!/(3x-1)!]}/{[(x-y-1)!/(x-1)!]-[(2x-y-1)!/(2x-1)!]}

obviously, ! is factorial.
kindly help me out on it or at least suggest something.
I'll be extremely grateful.

Eliza


		 	   		  
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Dear Berend,

Thankyou very much indeed for you reply. By taking help from your previous reply @ http://r.789695.n4.nabble.com/Simultaneous-equations-td2524645.html i was able to generate the following loop for the calculation of x=x[1] and y=x[2]. 


fun <- function(x) {

                f <- numeric(length(x))                                                                                 # read as:


f[1] <- 1-0.514-(gamma(1/x[1])*gamma(2/x[1]-1/x[2]))/(gamma(2/x[1])*gamma(1/x[1]-1/x[2]))

                f[2] <- 0.57-

(gamma(1/x[1]-1/x[2])/gamma(1/x[1])-3*gamma(2/x[1]-1/x[2])/gamma(2/x[1])+2*gamma(3/x[1]-1/x[2])/gamma(3/x[1]))/(gamma(1/x[1]-1/x[2])/gamma(1

/x[1])-gamma(2/x[1]-1/x[2])/gamma(2/x[1]))

                f

}


startx <- c(0.1,0.15) # start the answer search here

answers<-as.data.frame(nleqslv(startx,fun))

answers

What i cant understand is the concept involved for setting "startx". my x[1] should always be smaller than x[2] and they both should be less than 1. how can i demonstrate it to startx command line?

thanks for your help. I m grateful.

  Eliza

Subject: Re: [R] solving simultaneous Equations in R
From: bhh at xs4all.nl
Date: Wed, 11 Dec 2013 12:43:02 +0100
CC: r-help at r-project.org
To: eliza_botto at hotmail.com


On 11-12-2013, at 12:16, eliza botto <eliza_botto at hotmail.com> wrote:

Dear users of R,
I'm trying to solve the following 2 equations simultaneously in R for "x" and "y". I couldn't get through due to my limited knowledge of R.

3=1-[(x-1)!(2x-y-1)!/(2x-1)!(x-y-1)!] 

6={[(x-y-1)!/(x-1)!]-[3(2x-y-1)!/(2x-1)!]+[2(3x-y-1)!/(3x-1)!]}/{[(x-y-1)!/(x-1)!]-[(2x-y-1)!/(2x-1)!]}

obviously, ! is factorial.
kindly help me out on it or at least suggest something.
I'll be extremely grateful.

There are several packages that solve a system of equations.
ktsolve, nleqslv, BB, which you can find in CRAN Task views: "Numerical Mathematics? and ?Optimization?.

You will have to write your equations in standard R notation.
I can?t tell if your system is solvable.

Berend

Eliza



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