System of non-linear equations

Question

I am trying to solve a system of non-linear equations where number of valid solutions are unbounded. I am interested in only one valid result.

 y=zeros(6,1);
 y(1)=1000000*x(1)*x(4) + 100000*x(2)*x(4) -120;
 y(2)=1000000*x(1)*x(5) + 100000*x(2)*x(5) + 1000000*x(3)*x(5)-310;
 y(3)=200000*x(3)*x(6) - 200;
 y(4)=1000000*x(1)*x(4) + 1000000*x(1)*x(5) - 30;
 y(5)=100000*x(2)*x(4) + 100000*x(2)*x(5) - 300;
 y(6)=100000*x(3)*x(5) + 200000*x(3)*x(6) - 300;

is there any way in Matlab or R to solve these equations ? I tried solving it using octave's fsolve command but it never converges.

thanks

Answer 1

This system cannot be solved.

From $y(1)=0$, you can eliminate $x(4)$; from $y(2)=0$, you can eliminate $x(5)$; from $y(3)=0$, you can eliminate $x(6)$; from $y(4)=0$, you can eliminate $x(3)$; from $y(5)=0$, you can eliminate $x(2)$. When you put all of that in $y(6)$, you end with $0=-90$ !