Ответ учителя по предмету Алгебра
3x+5y=10
a=3; b=5
НОД(3;5)=1 => уравнение имеет решение в целых числах
В данном случае, частное решение найти не сложно:
3*20+5(-10)=10 => x₀=20; y₀=-10 — частное решение
Общее решение находим по формуле:
x=x₀+bk и y=y₀-ak, k∈Z
Получаем,
х=20+5k
y=-10-3k, k∈Z
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