title: Find any point on a 3D line defined by implicit equations
body: <p>The line is:</p>
  
  <p>Ax + By + Cz = D</p>
  
  <p>Ex + Fy + Gz = H</p>
  
  <p>I want any point (x,y,z) that satisfies those equations.</p>
  
  <p>I've tried by choosing one coordinate to set to zero, then solving for the other two. This works correctly except:</p>
  
  <p>1) I'm not sure of a reliable way to choose which coordinate to zero without causing numerical instability when some coefficients are zero or near zero.</p>
  
  <p>2) It involves a lot of if statements which makes the code messy and hard to test all combinations of conditions.</p>
  
  <p><strong>Edit:</strong> I don't care which point it finds. It doesn't have to allow all of them to be found.</p>