1: (x-1)(y+3)=11
=>(x-1;y+3)∈{(1;11);(11;1);(-1;-11);(-11;-1)}
=>(x;y)∈{(4;8);(12;-2);(0;-14);(-10;-4)}
2: (2x+1)(y-2)=3
=>(2x+1;y-2)∈{(1;3);(3;1);(-1;-3);(-3;-1)}
=>(2x;y)∈{(0;5);(2;3);(-2;-1);(-4;1)}
=>(x;y)∈{(0;5);(1;3);(-1;-1);(-2;1)}
3: xy+x-5y-7=0
=>x(y+1)-5y-5-2=0
=>x(y+1)-5(y+1)=2
=>(x-5)(y+1)=2
=>(x-5;y+1)∈{(1;2);(2;1);(-1;-2);(-2;-1)}
=>(x;y)∈{(6;1);(7;0);(4;-3);(3;-2)}
4: \(4x^2-4x+1-y^2=9\)
=>\(\left(2x-1\right)^2-y^2=9\)
=>(2x-1-y)(2x-1+y)=9
=>(2x-1-y;2x-1+y)∈{(1;9);(9;1);(-1;-9);(-9;-1);(3;3);(-3;-3)}
TH1: 2x-1-y=1 và 2x-1+y=9
=>2x-1-y+2x-1+y=1+9
=>4x-2=10
=>4x=12
=>x=3
2x-1-y=1
=>2*3-1-y=1
=>6-1-y=1
=>5-y=1
=>y=5-1=4
TH2: 2x-1-y=9 và 2x-1+y=1
=>2x-1-y+2x-1+y=9+1
=>4x-2=10
=>4x=12
=>x=3
2x-1+y=1
=>6-1+y=1
=>y+5=1
=>y=-4
TH3: 2x-1-y=-1 và 2x-1+y=-9
=>2x-1-y+2x-1+y=-1-9
=>4x-2=-10
=>4x=-8
=>x=-2
2x-1+y=-9
=>-4-1+y=-9
=>y-5=-9
=>y=-9+5=-4
TH4: 2x-1-y=-9 và 2x-1+y=-1
=>2x-1-y+2x-1+y=-9-1
=>4x-2=-10
=>4x=-8
=>x=-2
2x-1+y=-1
=>-4-1+y=-1
=>y-5=-1
=>y=-1+5=4
TH5: 2x-1-y=3 và 2x-1+y=3
=>2x-1-y+2x-1+y=6
=>4x-2=6
=>4x=8
=>x=2
2x-1-y=3
=>4-1-y=3
=>3-y=3
=>y=3-3=0
TH6: 2x-1-y=-3 và 2x-1+y=-3
=>2x-1-y+2x-1+y=-3-3
=>4x-2=-6
=>4x=-4
=>x=-1
2x-1-y=-3
=>-2-1-y=-3
=>-3-y=-3
=>y+3=3
=>y=0
