For the separation system in the figure below, The inlet mass flow rate is $20$ kilograms per hour and the mass fractions of each species in the inlet are $20\%,60\%$ and the rest make up $20\%.$ Compute the mass flow rates of each outlet stream $($kg$/$hour$).$

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Do your mass balances and compute a set of three algebraic equations to solve using the GAUSS ELIMINATION METHOD.