Question

20. Tìm x, y∈Z biết :

a) xy – 3x = -19 ;

b) 3x + 4y – xy = 16.

Answer 1

$a) xy-3x=-19$

$\Leftrightarrow x(y-3)=-19 =1.(-19)=(-19).1 =(-1).19=19.(-1)$

TH1: \(\left\{{}\begin{matrix}x=1\\y-3=-19\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-16\end{matrix}\right.\)

TH2: \(\left\{{}\begin{matrix}x=-19\\y-3=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-19\\y=4\end{matrix}\right.\)

TH3: \(\left\{{}\begin{matrix}x=-1\\y-3=19\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1\\y=22\end{matrix}\right.\)

TH4: \(\left\{{}\begin{matrix}x=19\\y-3=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=19\\y=2\end{matrix}\right.\)

Answer 2

Kẻ bảng cho bài này:

$b) 3x+4y-xy=16$

$\Leftrightarrow 3x-xy+4y-12=16-12$

$\Leftrightarrow x(3-y)+4(y-3)=4$

$\Leftrightarrow (x-4)(3-y)=4$

Vì $x,y \in \mathbb{Z} \Rightarrow x - 4$ và \(3-y\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)

Ta có bảng:

$$x-4$$	$$1$$	$$2$$	$$4$$	$$-2$$	$$-4$$
$$3-y$$	$$4$$	$$2$$	$$1$$	$$-2$$	$$-1$$
$$x$$	$$5$$	$$6$$	$$8$$	$$2$$	$$0$$
$$y$$	$$-1$$	$$1$$	$$2$$	$$5$$	$$4$$