`a,3x + 4y - x y = 16`
`⇔ 3x + 4y - xy - 12 = 16 -12`
`⇔ (3x - xy) - (12-4y)=4`
`⇔ x(3-y) - 4(3-y) = 4`
`⇔ (3-y)(x-4) = 4`
$\left \{ {{3-y=2} \atop {x-4=2}} \right.$
⇔ $\left \{ {{y=1} \atop {x=6}} \right.$
$\left \{ {{3-y=-2} \atop {x-4=-2}} \right.$
⇔ $\left \{ {{y=5} \atop {x=2}} \right.$
$\left \{ {{3-y=1} \atop {x-4=4}} \right.$
⇔ $\left \{ {{y=2} \atop {x=8}} \right.$
$\left \{ {{3-y=-1} \atop {x-4=-4}} \right.$
⇔ $\left \{ {{y=4} \atop {x=0}} \right.$
$\left \{ {{3-y=4} \atop {x-4=1}} \right.$
⇔ $\left \{ {{y=-1} \atop {x=5}} \right.$
$\left \{ {{3-y=-4} \atop {x-4=-1}} \right.$
⇔ $\left \{ {{y=7} \atop {x=3}} \right.$
`⇒ (y;x)∈{(2;8);(7;3);(4;0);(-1;5);(1;6);(5;2)}`
`b)xy - 3x=-19`
`⇔x(y-3)=-19=-1.19=-19.1`
$\left \{ {{x=1} \atop {y-3=-19}} \right.$
⇔ $\left \{ {{x=1} \atop {y=-16}} \right.$
$\left \{ {{x=-19} \atop {y-3=1}} \right.$
⇔ $\left \{ {{x=-19} \atop {y=4}} \right.$
$\left \{ {{x=-1} \atop {y-3=19}} \right.$
⇔ $\left \{ {{x=-1} \atop {y=22}} \right.$
$\left \{ {{x=19} \atop {y-3=-1}} \right.$
⇔ $\left \{ {{x=19} \atop {y=2}} \right.$
`⇒(x,y)∈{(-19;4);(19;2);(-1;22);(1;-16)}`
