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

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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

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