Решите в натуральных числах уравнение: 5x+y=30.

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

\[частное\ решение.\]

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

\[Для\ x:\ \ n \geq - 5;\ \ \ \ для\ y:\]

\[n \leq - 1 \Longrightarrow n = - 5;\ - 4;\ - 3;\ \]

\[- 2;\ - 1.\]

\[n = - 5:\]

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

\[= 25.\]

\[n = - 4:\]

\[x = 6 - 4 = 2;\ \ \ y = - 5 \bullet ( - 4) =\]

\[= 20.\]

\[n = - 3:\]

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

\[= 15.\]

\[n = - 2:\]

\[x = 6 - 2 = 4;\ \ y = - 5 \bullet ( - 2) =\]

\[= 10.\]

\[n = - 1:\]

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

\[= 5.\]

\[Ответ:x = 1,\ y = 25;\ \ x = 2,\ \]

\[y = 20;\ \ x = 3,\ y = 15;\ \ x = 4,\ \]

\[y = 10;\ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 5,y = 5.\]