1. Solve the following equations:
(i) $3 x_{1}+5 x_{2}=11$;
(ii) $60 x_{1}+123 x_{2}=25$;
(iii) $903 x_{1}+731 x_{2}=1106$;
(iv) $21 x_{1}+35 x_{2}=98$;
(v) $1402 x_{1}-1969 x_{2}=2$
1. (i) $x_{1}=2+5 t, x_{2}=1-3 t$; (ii) no solution, $(60,123)=3 \nmid 25$; (iii) no solution,
$$\begin{array}{l}
43=(903,731), 43 \nmid 1106 ; \text { (iv) } x_{1}=3+5 t, x_{2}=1-3 t ; \text { (v) } x_{1}=1778+1969 t, \\
x_{2}=1266+1402 t .
\end{array}$$