title: Solve a system of non-linear equations in Python (scipy.optimize.fsolve)
body: <p>I am trying to solve the following simple system of non-linear equations (<a href="http://www.mathsisfun.com/algebra/systems-linear-quadratic-equations.html" rel="nofollow noreferrer">Source(second example)</a>):</p>
  
  <pre><code>(I) y - x^2 = 7 - 5x
  (II) 4y - 8x = -21
  </code></pre>
  
  <p>which should have only one solution (x=3.5, y=1.75).</p>
  
  <p>My current approach using the <a href="https://docs.scipy.org/doc/scipy-0.18.0/reference/generated/scipy.optimize.fsolve.html#scipy.optimize.fsolve" rel="nofollow noreferrer">scipy</a> stack is the following:</p>
  
  <pre><code>from scipy.optimize import fsolve
  
  def equations(p):
      x, y = p
      return (y - x**2 -7 + 5*x, 4*y - 8*x + 21)
  
  x, y =  fsolve(equations, (5, 5))
  
  print(equations((x, y)))
  </code></pre>
  
  <p>and yields the following (which is not the result):</p>
  
  <pre><code>(0.0, 0.0)
  </code></pre>
  
  <p>I have already tried different starting estimates but it doesn't deliver the right  solution.</p>
  
  <p>What's wrong with my approach? Am I missing something?</p>
  
  <p>Thanks in advance!</p>