title: Findig a solution for a linear equation system which has more variable then equtions
body: <p>Let's divide the problem to 2 parts, the second one is optional.</p>
  
  <p>Part 1</p>
  
  <p>I have 3 linear equtions with N variables where N usually bigger then 3.</p>
  
  <ul>
  <li>x1*a+x2*b+x3*c+x4*d[....]xN*p = B1 </li>
  <li>y1*a+y2*b+y3*c+y4*d[....]yN*p = B2</li>
  <li>z1*a+z2*b+z3*c+z4*d[....]zN*p = B3</li>
  </ul>
  
  <p>Looking for (a,b,c,d,[...],p), others are constant.</p>
  
  <p>The standard Gaussian way won't work because the matrix will be wider then tall. Of course i can use it to eliminate 2 variables. Do you know an algorithm to find out a solution? (I only need one.) More 0s in the solution coefficients are better but not required.</p>
  
  <p>Part 2</p>
  
  <p>The coefficients in the solution must be non-negative.</p>
  
  <p>Requirements:
  The algorithm must be fast enough to run real time. (1800 per sec on an avrage pc). So trial and error method is a no go.
  The algorithm will be implemented in C# but feel free to use pseudo language if you want to write code.</p>