$\text { a }$) $\text { $\frac{1}{x}$ + $\frac{y}{3}$ = $\frac{1}{9}$ }$
$\text { ⇒ $\frac{1}{x}$ = $\frac{1}{9}$ - $\frac{y}{3}$ }$
$\text { ⇒ $\frac{1}{x}$ = $\frac{1}{9}$ - $\frac{3y}{9}$ }$
$\text { ⇒ $\frac{1}{x}$ = $\frac{1 - 3y}{9}$ }$
$\text { ⇒ x . (1 - 3y) = 9 }$
$\text { ⇒ $\left \{ {{9 \vdots x} \atop {9 \vdots 1 - 3y}} \right.$ }$
$\text { mà x,y ∈ Z }$
$\text { ⇒ x và 1 - 3y ∈ Ư(9) = {±1 ; ±3 ; ±9} }$
$\text { Ta có bảng: }$
$\text { x }$ $1$ $-1$ $3$ $-3$ $9$ $-9$
$\text { 1 - 3y }$ $9$ $-9$ $3$ $-3$ $1$ $-1$
$\text { y }$ $X$ $X$ $X$ $X$ $0$ $X$
$\text { Vậy (x,y) = (9,0) }$
$\text { b }$) $\text { xy + 2y - 3x = 5 }$
$\text { ⇒ y . (x + 2) - 3x - 3 . 2 = 5 - 3 . 2 }$
$\text { ⇒ y . (x + 2) - 3 . (x + 2) = -1 }$
$\text { ⇒ (x + 2)(y - 3) = -1 }$
$\text { ⇒ \(\left[ \begin{array}{l}\left \{ {{x + 2 = 1} \atop {y - 3 = -1}} \right.\\\left \{ {{x + 2 = -1} \atop {y - 3 =1}} \right.\end{array} \right.\) }$
$\text { ⇒ \(\left[ \begin{array}{l}\left \{ {{x = -1} \atop {y = 2}} \right.\\\left \{ {{x = -3} \atop {y = 4}} \right.\end{array} \right.\) }$
$\text { Vậy (x,y) ∈ {(-1;2),(-3;4)} }$
#Nothing is imposible#
#by dinhmanh312008#
#Cho mik hay nhất nhé#
