a: 2xy+x+2y=5
=>x(2y+1)+2y+1=6
=>(2y+1)(x+1)=6
=>\(\left(x+1;2y+1\right)\in\left\{\left(1;6\right);\left(6;1\right);\left(-1;-6\right);\left(-6;-1\right);\left(2;3\right);\left(3;2\right);\left(-2;-3\right);\left(-3;-2\right)\right\}\)
=>\(\left(x;y\right)\in\left\{\left(0;\dfrac{5}{2}\right);\left(5;0\right);\left(-2;-\dfrac{7}{2}\right);\left(-7;-1\right);\left(1;1\right);\left(2;\dfrac{1}{2}\right);\left(-3;-2\right);\left(-4;-\dfrac{3}{2}\right)\right\}\)
b: \(\dfrac{1}{x}+\dfrac{y}{3}=\dfrac{2}{5}\)
=>\(\dfrac{3+xy}{3x}=\dfrac{2}{5}\)
=>\(5\left(xy+3\right)=6x\)
=>6x-5xy=15
=>x(6-5y)=15
=>x(5y-6)=-15
=>(x;5y-6)\(\in\){(1;-15);(-15;1);(-1;15);(15;-1);(3;-5);(-5;3);(-3;5);(5;-3)}
=>\(\left(x;y\right)\in\left\{\left(1;-\dfrac{9}{5}\right);\left(-15;\dfrac{7}{5}\right);\left(-1;\dfrac{21}{5}\right);\left(15;1\right);\left(3;\dfrac{1}{5}\right);\left(-5;\dfrac{9}{5}\right);\left(-3;\dfrac{11}{5}\right);\left(5;\dfrac{3}{5}\right)\right\}\)
