4x-y+2xy=14
=>4x+2xy-y=14
=>2x(y+2)-y-2=12
=>(2x-1)(y+2)=12
=>\(\left(2x-1\right)\left(y+2\right)=1\cdot12=12\cdot1=\left(-1\right)\cdot\left(-12\right)=\left(-12\right)\cdot\left(-1\right)=2\cdot6=6\cdot2=\left(-2\right)\cdot\left(-6\right)=\left(-6\right)\cdot\left(-2\right)=3\cdot4=4\cdot3=\left(-3\right)\cdot\left(-4\right)=\left(-4\right)\cdot\left(-3\right)\)
=>(2x-1;y+2)\(\in\){(1;12);(12;1);(-1;-12);(-12;-1);(2;6);(6;2);(-2;-6);(-6;-2);(3;4);(-3;-4);(4;3);(-4;-3)}
=>\(\left(x;y\right)\in\left\{\left(1;10\right);\left(\dfrac{13}{2};-1\right);\left(0;-14\right);\left(-\dfrac{11}{2};-3\right);\left(\dfrac{3}{2};4\right);\left(\dfrac{7}{2};0\right);\left(-\dfrac{1}{2};-8\right);\left(-\dfrac{5}{2};-4\right);\left(2;2\right);\left(-1;-6\right);\left(\dfrac{5}{2};1\right);\left(-\dfrac{3}{2};-5\right)\right\}\)
4x-y+2xy=14
=>4x+2xy-y=14
=>2x(y+2)-y-2=12
=>(2x-1)(y+2)=12
=>(2x−1)(y+2)=1⋅12=12⋅1=(−1)⋅(−12)=(−12)⋅(−1)=2⋅6=6⋅2=(−2)⋅(−6)=(−6)⋅(−2)=3⋅4=4⋅3=(−3)⋅(−4)=(−4)⋅(−3)(2�−1)(�+2)=1⋅12=12⋅1=(−1)⋅(−12)=(−12)⋅(−1)=2⋅6=6⋅2=(−2)⋅(−6)=(−6)⋅(−2)=3⋅4=4⋅3=(−3)⋅(−4)=(−4)⋅(−3)
=>(2x-1;y+2)∈∈{(1;12);(12;1);(-1;-12);(-12;-1);(2;6);(6;2);(-2;-6);(-6;-2);(3;4);(-3;-4);(4;3);(-4;-3)}
=>