MATLAB: I am not able to solve this system of two non-linear equations. Any ideas

fsolve

function [ F ] = roots( x )
%UNTITLED2 Summary of this function goes here
%   Detailed explanation goes here
F(1) = (2.6-95/(x(1)-292.96))*x(2) + (95*x(1))/(x(1)-292.96) - 6.8297e3;
F(2) = -(2.6-95/(x(1)-292.96))*x(2) +2.7831e4/(x(1)-292.96) + 3.7105e3;
end
fun = @roots;
x0 = 100*ones(1, 2);
x = fsolve(fun, x0);
when i run the code it says that the solver stopped prematurely and i get wrong values for x(1) and x(2). I tried to increase the MaxFunEvals and the MaxIter as follows:
fun = @roots;
x0 = 100*ones(1, 2);
options = optimset('MaxFunEvals',10000);
options = optimset(options,'MaxIter',10000);
x = fsolve(fun, x0, options);
However, i am still getting the same error. Any ideas on how to solve this issue ?

Best Answer

Seems trivial.
Solve the second equation, isolating y. You would get this:
y = (927625*x - 264799270)/(650*x - 214174)
Now, substitute into the first equation. You would get this:
(95*x)/(x - 7324/25) - ((927625*x - 264799270)*(95/(x - 7324/25) - 13/5))/(650*x - 214174) - 68297/10 == 0
That yields only one solution for x.
x = 117703979/378025
Then recover y, which would be:
y = -14535055165/7128864
Pencil and paper should suffice.
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