5x + y − xy = 2
y(1 − x) = 2 − 5x
$y = \frac{2 - 5x}{1 - x} = \frac{5x - 2}{x - 1} = \frac{5x - 5 + 3}{x - 1} = \frac{5(x - 1) + 3}{x - 1} = 5 + \frac{3}{x - 1}$
Дробь $\frac{3}{x - 1}$ будет целой при x − 1 = {±1; ±3}.
x − 1 = −1
x = 0
$y = 5 + \frac{3}{0 - 1} = 5 - 3 = 2$
 
x − 1 = 1
x = 2
$y = 5 + \frac{3}{2 - 1} = 5 + 3 = 8$
 
x − 1 = −3
x = −2
$y = 5 + \frac{3}{-2 - 1} = 5 - 1 = 4$
 
x − 1 = 3
x = 4
$y = 5 + \frac{3}{4 - 1} = 5 + 1 = 6$
Ответ: {(−2;4), (0;2), (2;8), (4;6)}.

xy − x + y = 8
y(x + 1) = x + 8
$y = \frac{x + 8}{x + 1} = \frac{x + 1 + 7}{x + 1} = 1 + \frac{7}{x + 1}$
Дробь $\frac{7}{x + 1}$ будет целой при x + 1 = {±1; ±7}.
x + 1 = −1
x = −2
$y = 1 + \frac{7}{-2 + 1} = 1 + \frac{7}{-1} = 1 - 7 = -6$
 
x + 1 = 1
x = 0
$y = 1 + \frac{7}{0 + 1} = 1 + \frac{7}{1} = 1 + 7 = 8$
 
x + 1 = −7
x = −8
$y = 1 + \frac{7}{-8 + 1} = 1 + \frac{7}{-7} = 1 - 1 = 0$
 
x + 1 = 7
x = 6
$y = 1 + \frac{7}{6 + 1} = 1 + \frac{7}{7} = 1 + 1 = 2$
Ответ: {(−8;0), (−2;−6), (0;8), (6;2)}.