Can someone show me how to solve this system of equations? \begin{align} 4X+12Y-7Z-20W&=22 \\ 3X+9Y-5Z-28W&=30 \end{align}

Does this mean that there are two free variables here?

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    $\begingroup$ Yes, that's it. $\endgroup$ – cjferes Aug 25 '14 at 13:15
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    $\begingroup$ And one of the free variables has to be either $X$ or $Y$. $\endgroup$ – Arthur Aug 25 '14 at 13:16
  • $\begingroup$ Fix two of them (treat them as constants) and solve the two linear equations for the two remaining unknowns. But take care : see what happens if you multiply the first equation by $3$ and the second by $3$. $\endgroup$ – Claude Leibovici Aug 25 '14 at 14:58

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