problem: If \begin{align*}
  4x-y+2z&=7,\\
  6x+3y+3z&=5,
  \end{align*} compute $y$.
solution: Let $w=2x+z$.  The equations become \begin{align*}
  2w-y&=7,\\
  3w+3y&=5.
  \end{align*} Subtracting twice the second equation from three times the first equation,  $$6w-3y-6w-6y=21-10\Rightarrow -9y=11.$$ Thus $y=\boxed{-\frac{11}{9}}$.