
  You want to solve this nonlinear system of equations :

        a 1/X + b 1/Y + c 1/Z = d
        e 1/X + f 1/Y + g 1/Z = h
        i 1/X + j 1/Y + k 1/Z = l

  If you write :

               1/X = x
               1/Y = y
               1/Z = z
    
  You can rewrite the system :

        a x + b y + c z = d
        e x + f y + g z = h
        i x + j y + k z = l

 Which is a linear system of equation in x, y, z.

 Suppose, the solution of the system is :

                    x = r
                    y = s
                    z = t 

 you can write
                  1/X = r    if r =  1/2    X = 2 
                  1/Y = s    if s = -3/4    Y = -4/3
                  1/Z = t    ...
 
 The bad value for r, s, t is : 0/1
