How to solve a pair of nonlinear equations using Python?
You can use openopt package and its NLP method. It has many dynamic programming algorithms to solve nonlinear algebraic equations consisting:  
goldenSection, scipy_fminbound, scipy_bfgs, scipy_cg, scipy_ncg, amsg2p, scipy_lbfgsb, scipy_tnc, bobyqa, ralg, ipopt, scipy_slsqp, scipy_cobyla, lincher, algencan, which you can choose from.  
Some of the latter algorithms can solve constrained nonlinear programming problem.
So, you can introduce your system of equations to openopt.NLP() with a function like this:  
lambda x: x[0] + x[1]**2 - 4, np.exp(x[0]) + x[0]*x[1]
What's the (best) way to solve a pair of non linear equations using Python. (Numpy, Scipy or Sympy)
eg:


x+y^2 = 4
e^x+ xy = 3


A code snippet which solves the above pair will be great