title: Solve a system of equations depending on a set of parameters with Mathematica
body: <p>Using Mathematica, I want to solve a system of nonlinear equations like</p>
  
  <pre><code>f(x,y;m)=0
  g(x,y;m)=0
  </code></pre>
  
  <p>where m is an external parameter on which the equations depends on.
  As the equations are very hard, what I do is to explicitly fix m, above all, and then find a solution for that specific value of m (by FindRoot[]). But this is very slow and inefficient (and more specifically in my case, where indeed I have three parameters).</p>
  
  <p>What I would like is an automatic method that studies numerically the solution for a discrete set of values ​​for m, that fixes it without that I explicitly change it from time to time. So that I would get all together the solutions for those values ​​of m.</p>
  
  <p>It would be nice also that a similar procedure can be applied to the initial seeds for FindRoot [], since in my case I get several solutions changing the latter, and so there are different solutions for that value of m, and so similarly I would like to have all the solutions for a given set of initial seeds.</p>
  
  <p>Is it possible to do such a thing? How?</p>
  
  <p>Many thanks</p>