17. Find all positive solutions of the following system of indeterminate equations:
(i) $2 x_{1}+x_{2}+x_{3}=100, 3 x_{1}+5 x_{2}+15 x_{3}=270$;
(ii) $x_{1}+x_{2}+x_{3}=31, x_{1}+2 x_{2}+3 x_{3}=41$.
17. (i) $x_{1}=40, x_{2}=15, x_{3}=5$;
(ii) $\{22,8,1\},\{23,6,2\},\{24,4,3\},\{25,2,4\}$.