Đáp án:a)(x;y)=(1;-16); (1;22); (19;2); (-19;4)
b)(x;y)=(-3;-1); (-5;7); (-2;1); (-6;5); (0;2); (-8;4)
Giải thích các bước giải:
a)xy-3x=-19⇒x(y-3)=-19
⇒x; y-3∈U(-19)={-1;1;-19;19}
⇒(1)$\left \{ {{x=1} \atop {y-3=-19}} \right.$ ⇔$\left \{ {{x=1} \atop {y=-16}} \right.$
⇒(2)$\left \{ {{x=-1} \atop {y-3=19}} \right.$ ⇔$\left \{ {{x=1} \atop {y=22}} \right.$
⇒(3)$\left \{ {{x=19} \atop {y-3=-1}} \right.$ ⇔$\left \{ {{x=19} \atop {y=2}} \right.$
⇒(4)$\left \{ {{x=-19} \atop {y-3=1}} \right.$ ⇔$\left \{ {{x=-19} \atop {y=4}} \right.$
⇒(x;y)=(1;-16); (1;22); (19;2); (-19;4)
b)3x+4y-xy=16
⇒3x-xy+4y-12=4
⇒(x+4)(3-y)=4
⇒x+4; 3-y∈U(4)={-1;1;-2;2;-4;4}
⇒(1)$\left \{ {{x+4=1} \atop {3-y=4}} \right.$ ⇔$\left \{ {{x=-3} \atop {y=-1}} \right.$
⇒(2)$\left \{ {{x+4=-1} \atop {3-y=-4}} \right.$ ⇔$\left \{ {{x=-5} \atop {y=7}} \right.$
⇒(3)$\left \{ {{x+4=2} \atop {3-y=2}} \right.$ ⇔$\left \{ {{x=-2} \atop {y=1}} \right.$
⇒(4)$\left \{ {{x+4=-2} \atop {3-y=-2}} \right.$ ⇔$\left \{ {{x=-6} \atop {y=5}} \right.$
⇒(5)$\left \{ {{x+4=4} \atop {3-y=1}} \right.$ ⇔$\left \{ {{x=0} \atop {y=2}} \right.$
⇒(6)$\left \{ {{x+4=-4} \atop {3-y=-1}} \right.$ ⇔$\left \{ {{x=-8} \atop {y=4}} \right.$
⇒(x;y)=(-3;-1); (-5;7); (-2;1); (-6;5); (0;2); (-8;4)
