Chapter 3 - The Structure of Crystalline Solids - Questions and Problems - Page 100: 3.43

$U=\frac{1}{5}(6u-3v)$ $V=\frac{1}{5}(6v-3u)$ $W=w$

$u=\frac{1}{3}(2U-V)$ $v=\frac{1}{3}(2V-U)$ $t=-(u+v)$ $w=W$ after solving the above two equations as linear equations of two variables, we find: $U=\frac{1}{5}(6u-3v)$ $V=\frac{1}{5}(6v-3u)$ $W=w$