You can take the first and the last equation since then you deal with only two unknowns and two equations.
You can use elimination, by first removing the fractions, ie. multiply throughout by 7, then the LCM of 2 and 3 is 6, multiply the first one by 3 and the last equation by 2 throughout. Add both to get F_b.
Then solve for F_c, and used both to get F_r
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