HMMT 2002 A7

The real numbers $x, y, z, w$ satisfy

$$\begin{aligned} 2 x+y+z+w & =1 \\ x+3 y+z+w & =2 \\ x+y+4 z+w & =3 \\ x+y+z+5 w & =25 . \end{aligned}$$

Find the value of $w$.