\(\dfrac{3}{x}+\dfrac{y}{3}=\dfrac{5}{6}\)
=>\(\dfrac{9+xy}{3x}=\dfrac{5}{6}\)
=>\(\dfrac{9+xy}{x}=\dfrac{5}{2}\)
=>\(5x=2\left(xy+18\right)\)
=>5x-2xy=36
=>x(5-2y)=36
mà 5-2y lẻ
nên \(x\left(5-2y\right)=36\cdot1=\left(-36\right)\cdot\left(-1\right)=12\cdot3=\left(-12\right)\cdot\left(-3\right)=4\cdot9=\left(-4\right)\cdot\left(-9\right)\)
=>\(\left(x;5-2y\right)\in\left\{\left(36;1\right);\left(-36;-1\right);\left(12;3\right);\left(-12;-3\right);\left(4;9\right);\left(-4;-9\right)\right\}\)
=>\(\left(x;y\right)\in\left\{\left(36;2\right);\left(-36;3\right);\left(12;1\right);\left(-12;4\right);\left(4;-2\right);\left(-4;7\right)\right\}\)
