# solving a system of 2 equations with 4 variables

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?

• Yes, that's it. – cjferes Aug 25 '14 at 13:15
• And one of the free variables has to be either $X$ or $Y$. – Arthur Aug 25 '14 at 13:16
• 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 $3$. – Claude Leibovici Aug 25 '14 at 14:58