title: Solving non-linear equations in python
body: <p>I have 4 non-linear equations with three unknowns <code>X</code>, <code>Y</code>, and <code>Z</code> that I want to solve for. The equations are of the form:</p>
  
  <pre><code>F(m) = X^2 + a(m)Y^2 + b(m)XYcosZ + c(m)XYsinZ
  </code></pre>
  
  <p>...where <code>a</code>, <code>b</code> and <code>c</code> are constants which are dependent on each value of <code>F</code> in the four equations. </p>
  
  <p>What is the best way to go about solving this? </p>