Question

как решать уравнение xy=3x+y

Answer 1

3x + y - xy = 0

x(3 - y) - (3 - y) = -3

(x - 1)(3 - y) = -3

{x-1 = 3 => x = 4
{3-y = -1 => y = 4

{x-1 = -3 => x = -2
{3-y = 1 => y = 2

{x-1 = 1 => x = 2
{3-y = -3 => y = 6

{x-1 = -1 => x = 0
{3-y = 3 => y = 0

Это решения в целых числах

если общее, то y  = 3x/(x-1), x≠1

Ответ: (0; 0); (2; 6); (-2; 2); (4; 4)