Решите в натуральных числах уравнение: 5x+y=50.

\[5x + y = 50;\ \ \ (10;0) -\]

\[частное\ решение.\]

\[x = 10 + n;\ \ y = - 5n;\ \ \ n \in Z.\]

\[Для\ x:\ \ n \geq - 9;\ \ для\ y:\ \]

\[\ n \leq - 1 \Longrightarrow n = - 9; - 8; - 7; - 6;\]

\[- 5; - 4; - 3; - 2; - 1.\]

\[n = - 9:\]

\[x = 10 - 9 = 1;\ \ \]

\[y = - 5 \bullet ( - 9) = 45.\]

\[n = 8:\]

\[x = 10 - 8 = 2;\ \]

\[\ y = - 5 \bullet ( - 8) = 40.\]

\[n = - 7:\]

\[x = 10 - 7 = 3;\ \ \]

\[y = - 5 \bullet ( - 7) = 35.\]

\[n = - 6:\]

\[x = 10 - 6 = 4;\ \ \]

\[\ y = - 5 \bullet ( - 6) = 30.\]

\[n = - 5:\]

\[x = 10 - 5 = 5;\ \ \]

\[\ y = - 5 \bullet ( - 5) = 25.\]

\[n = - 4:\]

\[x = 10 - 4 = 6;\ \]

\[\ y = - 5 \bullet ( - 4) = 20.\]

\[n = - 3:\]

\[x = 10 - 3 = 7;\ \ \]

\[y = - 5 \bullet ( - 3) = 15.\]

\[n = - 2:\]

\[x = 10 - 2 = 8;\ \ \ \]

\[y = - 5 \bullet ( - 2) = 10.\]

\[n = - 1:\]

\[x = 10 - 1 = 9;\ \ \ \]

\[y = - 5 \bullet ( - 1) = 5.\]

\[Ответ:x = 1,y = 45;\ \ \]

\[x = 2,\ y = 40;x = 3,\ y = 35;\]

\[x = 4,\ y = 30;\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ x = 5,y = 25;\ \ x = 6,\]

\[\ y = 20;x = 7,\ y = 15;x = 8,\ \]

\[y = 10;\]

\[\ \ \ \ \ \ \ \ \ x = 9,\ y = 5.\]