=>x(2y+1)-3y-1,5=2,5
=>(y+0,5)(2x-3)=2,5
=>(2y+1)(2x-3)=5
=>\(\left(2x-3;2y+1\right)\in\left\{\left(1;5\right);\left(5;1\right);\left(-1;-5\right);\left(-5;-1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(2;2\right);\left(4;0\right);\left(1;-3\right);\left(-1;-1\right)\right\}\)
\(2xy+x-3y=4\)
\(\Leftrightarrow4xy+2x-6y=8\)
\(\Leftrightarrow4xy+2x-6y-3=5\)
\(\Leftrightarrow2x\left(2y+1\right)-3\left(2y+1\right)=5\)
\(\Leftrightarrow\left(2x-3\right)\left(2y+1\right)=5\)
| 2x-3 | -5 | -1 | 1 | 5 |
| 2y+1 | -1 | -5 | 5 | 1 |
| x | -1 | 1 | 2 | 4 |
| y | -1 | -3 | 2 | 0 |
Vậy pt có các cặp nghiệm nguyên \(\left(x;y\right)=\left(-1;-1\right);\left(1;-3\right);\left(2;2\right);\left(4;0\right)\)
