How can I 'invert' a 2-input, 2-output system

I have a set of data contained in two tables, such that

   Table 1 uses M1 and M2 as inputs, and gives F1 as the output
   Table 2 uses M1 and M2 as inputs, and gives F2 as the output

I would like to 'invert' these tables, such that

   Table 1 uses F1 and F2 as inputs, and gives M1 as the output
   Table 2 uses F1 and F2 as inputs, and gives M2 as the output

Thank you, Katherine