title: non-negative integer solutions to system of linear equations in mathematica
body: <p>Related to <a href="https://stackoverflow.com/questions/4987972/how-to-solve-for-all-non-negative-integer-xis-in-mathematica">my previous question</a>, just wonder how to solve a system of linear equations with non-negative integral solutions, for example:</p>
  
  <pre><code>c11*x+c12*y+c13*z=d1
  c21*x+c22*y+c23*z=d2
  </code></pre>
  
  <p>Thanks a lot!</p>
  
  <p><strong>Edit</strong></p>
  
  <p>I meant efficiently. For example, I could have used <code>FrobeniusSolve</code> to get two solution lists and try to find the intersection. But sometimes, the individual solution list is probably hugely large. Or try to verify each individual solution returned by one <code>FrobeniusSolve</code> to see whether they satisfy all the remaining equations, but that suffers from the same drawback.</p>