Giải thích các bước giải:
a.$5(x+y)+2=3xy\to 5x+5y-3xy+2=0$
$\to x(5-3y)+5y+2=0$
$\to 3x(5-3y)+15y+6=0$
$\to 3x(5-3y)+15y-25=-31$
$\to 3x(5-3y)+5(3y-5)=-31$
$\to (3x-5)(5-3y)=-31$
$\to (3x-5)(3y-5)=31$
$\to (3x-5,3y-5)=\{(31,1),(1,31)\}$ vì $x,y>0$
$\to (x,y)=\{(12,2),(2,15)\}$
b.$2(x+y)=3xy$
$\to 2x+2y-3xy=0$
$\to x(2-3y)+2y=0$
$\to 3x(2-3y)+6y=0$
$\to 3x(3y-2)-6y=0$
$\to 3x(3y-2)-(6y-4)=4$
$\to 3x(3y-2)-2(3y-2)=4$
$\to (3x-2)(3y-2)=4$
$\to (3x-2,3y-2)\in\{(4,1),(1,4),(-2,-2)\}$
Vì $3x-2, 3y-2$ chia 3 dư 2
$\to (x,y)\in\{(2,1),(1,2), (0,0)\}$
