How to solve this non-linear system of equations?

[parisse]

You can not use conditions for multivariate systems with approx coefficients, you can only give an initial guess, and if it is not far from a solution, fsolve will return a solution up to machine precision. Your solution does not seem to work by the way:
fsolve([eq1,eq2],[x,y],[11.3,302.5]) returns [-3.39546756307,313.410392968]
(with degree mode)