Finding solution

Dear all, I have a system of simultaneous equations with 2 unknowns as
follows:



x*y + (1-x) = 0.05

x*(y - .5)^2 + (1-x)*0.6 = 0.56^2



Ofcourse I can do it manually however wondering whether there is any direct
way in R available to get the solution of this system?

Not really (can't vouch for all 3000+ packages, though...)

You can sometimes get away with converting  to a minimization problem:

f <- function(xy,x=xy[1],y=xy[2])(x*y + (1-x) - 0.05)^2+(x*(y - .5)^2 + (1-x)*0.6 - 0.56^2)^2
optim(par=c(0,0),f,method="BFGS")$par

[1]  0.91674574 -0.03627402

$value
[1] 5.351777e-13

$counts
function gradient 
     39       13 

$convergence
[1] 0

$message
NULL


Notice that there is some risk of falling into a local minimum which has nothing to do with the solution. Always check that the minimum actually comes out as zero.

Thanks and regards,




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Dear all, I have a system of simultaneous equations with 2 unknowns as
follows:

x*y + (1-x) = 0.05

x*(y - .5)^2 + (1-x)*0.6 = 0.56^2

Ofcourse I can do it manually however wondering whether there is any
direct
way in R available to get the solution of this system?

Look at the Task view Optimization.

Two packages for solving systems of nonlinear equations are available: 
nleqslv and BB.

Berend


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