Đáp án:a)(x;y)=(-2;2); (-4;-4); (0;2); (-4;-2)

b)(x;y)=(5;-1); (3;-7); (6;1); (2;5); (8;2); (0;4)

c)(x;y)=(2;3); (0;-7); (6;-1); (-4;-3)

Giải thích các bước giải:

 a)(x+3)(y+1)=3

⇒x+3;y+1∈U(3)

⇒x+3;y+1∈U(3)={-1;1;-3;3}

⇒(1)$\left \{ {{x+3=1} \atop {y+1=3}} \right.$ ⇔$\left \{ {{x=-2} \atop {y=2}} \right.$ 

⇒(2)$\left \{ {{x+3=-1} \atop {y+1=-3}} \right.$ ⇔$\left \{ {{x=-4} \atop {y=-4}} \right.$

⇒(3)$\left \{ {{x+3=3} \atop {y+1=1}} \right.$ ⇔$\left \{ {{x=0} \atop {y=2}} \right.$

⇒(4)$\left \{ {{x+1=-3} \atop {y+1=-1}} \right.$ ⇔$\left \{ {{x=-4} \atop {y=-2}} \right.$

⇒(x;y)=(-2;2); (-4;-4); (0;2); (-4;-2)

b)3x+4y-xy=16⇔3x-12-4y-xy=4⇔ (x-4)(3-y)=4

⇒x-4; 3-y∈U(4)={-1;1;-2;2;-4;4}

⇒(1)$\left \{ {{x-4=1} \atop {3-y=4}} \right.$ ⇔$\left \{ {{x=5} \atop {y=-1}} \right.$

⇒(2)$\left \{ {{x-4=-1} \atop {3-y=-4}} \right.$ ⇔$\left \{ {{x=3} \atop {y=-7}} \right.

⇒(3)$\left \{ {{x-4=2} \atop {3-y=2}} \right.$ ⇔$\left \{ {{x=6} \atop {y=1}} \right.$

⇒(4)$\left \{ {{x-4=-2} \atop {3-y=-2}} \right.$ ⇔$\left \{ {{x=2} \atop {y=5}} \right.$

⇒(5)$\left \{ {{x-4=4} \atop {3-y=1}} \right.$ ⇔$\left \{ {{x=8} \atop {y=2}} \right.$

⇒(6)$\left \{ {{x-4=-4} \atop {3-y=-1}} \right.$ ⇔$\left \{ {{x=0} \atop {y=4}} \right.$

⇒(x;y)=(5;-1); (3;-7); (6;1); (2;5); (8;2); (0;4)

c) xy+2x-y-7=0⇔ xy+2x-y-2=5⇔ (x-1)(y+2)=5

⇒x-1;y+2∈U(5)={-1;1;-5;5}

⇒(1)$\left \{ {{x-1=1} \atop {y+2=5}} \right.$ ⇔$\left \{ {{x=2} \atop {y=3}} \right.$

⇒(2)$\left \{ {{x-1=-1} \atop {y+2=-5}} \right.$ ⇔$\left \{ {{x=0} \atop {y=-7}} \right.$

⇒(3)$\left \{ {{x-1=5} \atop {y+2=1}} \right.$ ⇔$\left \{ {{x=6} \atop {y=-1}} \right.$

⇒(4)$\left \{ {{x-1=-5} \atop {y+2=-1}} \right.$ ⇔$\left \{ {{x=-4} \atop {y=-3}} \right.$

⇒(x;y)=(2;3); (0;-7); (6;-1); (-4;-3)