# System of non-linear equations

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

• I trust the answer below that the above cannot be solved, so I'll just say this for future reference. In Matlab you could use fminsearch to solve something like this by defining the cost function to be the sum of the squared error from each equality constraint. For instance, if $y_1 = f_1(\mathbf{x})$ and $y_2 = f_2(\mathbf{x})$, then the cost function would be $c = ( y_1 - f_1(\mathbf{x}))^2 + ( y_2 - f_2(\mathbf{x}))^2$. – AnonSubmitter85 Feb 2 '14 at 18:06

## 1 Answer

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 $0=-90$ !