I need to solve two nonlinear equations simultaneously

Equations are as below F(1)=(1/x)*34+34*log(1510247/y)-34*((1510247/y)^x)*log(1510247/y)-63740*((6099707071/y)^x)*log(6099707071/y) F(2)=(-x/y)*34+(x/y)*34*(1510247/y)^x+(x/y)*63740*(6099707071/y)^x

Answer 1

[Roger Stafford]

If you have the Optimization Toolbox, you can use fsolve to find an accurate simultaneous solution for the two equations. You can read about it at:

https://www.mathworks.com/help/optim/ug/fsolve.html

To use it you will need an initial rough estimate of the solution. To obtain that rough estimate I would recommend you use the contour function for both equations seeking simultaneous zero value contours, and see where the two respective contours cross (use “hold on”.) You can read about the contour function at:

https://www.mathworks.com/help/matlab/ref/contour.html

[Hint: For the contour grid I recommend you use x values in the neighborhood of multiples of 10^(-5) and y values somewhere in the neighborhood of multiples of 10^6. I think the two contours will cross somewhere in that area.]