Решите в натуральных числах уравнение: 6x+y=30.

\[6x + y = 30;\ \ (5;0) -\]

\[частное\ решение.\]

\[x = 5 + n;\ \ y = - 6n;\ \ n \in Z.\]

\[Для\ x:\ \ \ n \geq - 4;\ \ \ \ для\ y:\ \ \]

\[n \leq - 1 \Longrightarrow n = - 4;\ - 3; - 2; - 1.\]

\[n = - 4:\]

\[x = 5 - 4 = 1;\ \ y = - 6 \bullet ( - 4) =\]

\[= 24.\]

\[n = - 3:\]

\[x = 5 - 3 = 2;\ \ y = - 6 \bullet ( - 3) =\]

\[= 18.\]

\[n = - 2:\]

\[x = 5 - 2 = 3;\ \ y = - 6 \bullet ( - 2) =\]

\[= 12.\]

\[n = - 1:\]

\[x = 5 - 1 = 4;\ \ y = - 6 \bullet ( - 1) =\]

\[= 6.\]

\[Ответ:x = 1,\ y = 24;\ \ x = 2,\]

\[\ y = 18;\ \ x = 3,\ y = 12;\ \ x = 4,\ \]

\[y = 6.\]