a: xy+3x-7y=21

=>x(y+3)-7y-21=0

=>x(y+3)-7(y+3)=0

=>(x-7)(y+3)=0

=>\(\begin{cases}x-7=0\\ y+3=0\end{cases}\Rightarrow\begin{cases}x=7\\ y=-3\end{cases}\)

b: xy+3x-2y=11

=>x(y+3)-2y-6=11-6

=>x(y+3)-2(y+3)=5

=>(x-2)(y+3)=5

=>(x-2;y+3)∈{(1;5);(5;1);(-1;-5);(-5;-1)}

=>(x;y)∈{(3;2);(7;-2);(1;-8);(-3;-4)}

a)xy+3x-2y=12

=>x(y+3)-2y=12

=>x(y+3)-2(y+3)=6

<=>(x-2)(y+3)=6

th1:(x-2)=1 <-> x=3

      (y+3)=6 <-> y=3

th2:(x-2)=6 <-> x=8

      (y+3)=1 <-> y=-2

th3:(x-2)=2 <-> x=4

      (y+3)=3 <-> y=0

th4:(x-2)=3 <-> x=5

      (y+3)=2 <-> y=-1

Vậy (x,y) thuộc  {(3;3);(8;-2);(4;0);(5;-1)

Các câu khác làm tương tự

uuttqquuậậyy gửi từng bài thì có mà hết lượt gửi câu hỏi à

  a, xy+3x-7y=21.                                           => x(y+3) - 7(y+3) = 0.                                       => (x-7)(y+3)=0.                                               => x=7 , và với mọi y.  Hoặc y=3 với mọi x

cái này dễ quá aaa

dễ thì làm đi

a.
xy + 3x - 2y - 6 = 5
=>x(y + 3) - 2(y + 3) = 5
=>(x - 2)(y + 3) = 5.
Vì x, y thuộc Z nên x - 2, y + 3 thuộc Z
=> x - 2, y + 3 thuộc ước nguyên của 5
Lập bảng : 

Vậy ......

b. Làm tương tự câu a.

c. Ta có x + y = 3 và x - y = 15
Bài này là tổng hiệu của cấp 1, áp dụng cách làm đó thì ta được số lớn là x = (3 + 15) : 2 = 9
Số bé là y = 9 - 15 = -6

d. Ta có : |x| + |y| = 1
=>|x| = 1 - |y|
Vì |x|, |y| >= 0 và |x| = 1 - |y| nên 0 =< |x|, |y| =< 1
Vì x, y thuộc Z nên x = 0 thì y = 1 hoặc -1 và ngược lại y = 0 thì x = 1 hoặc -1

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a.

$xy=-21=7.(-3)=(-7).3=3.(-7)=(-3).7=21.(-1)=(-21).1=(-1).21=1(-21)$

Do đó $(x,y)=(7,-3); (-7,3); (3,-7); (-3,7); (21,-1); (-21,1); (-1,21); (1,-21)$

b.

$(x+5)(y-3)=14=1.14=14.1=(-14)(-1)=(-1)(-14)=2.7=7.2=(-2)(-7)=(-7)(-2)$

Do đó:

$(x+5,y-3)=(1,14); (14,1); (-14,-1); (-1,-14); (2,7); (7,2); (-2,-7); (-7,-2)$

Đến đây thì đơn giản rồi.

c.

$x(y-2)=-19$, bạn làm tương tự

d. Tương tự

bạn ơi hình như đề bạn viết nó có sai sai sao ý =(

+@

 xy+3x-2y=21 <=> xy - 7y + 3x - 21 = -5y

<=> y(x-7) + 3 (x-7) = - 5y

(x-7)(y+3) = - 5y

* Nếu y là SNT => x-7 = y và y + 3 = -5 hoặc x-7 = -y và y + 3 = 5

+ x-7 = y và y + 3 = -5 => y = -8; x = -1

+ x-7 = - y và y + 3 = 5 => y = 2 và x = 5

* Nếu y là hợp số ....Để nghĩ tiếp, jờ phải lên lớp rồi