\(6x-y+3xy=15\)
\(\Leftrightarrow\left(6x+3xy\right)-y=15\)
\(\Leftrightarrow3x\left(2+y\right)-y=13+2\)
\(\Leftrightarrow3x\left(2+y\right)-y-2=13\)
\(\Leftrightarrow3x\left(2+y\right)-\left(y+2\right)=13\)
\(\Leftrightarrow\left(2+y\right)\left(3x-1\right)=13\)
\(\Rightarrow\left(2+y\right);\left(3x-1\right)\inƯ\left(13\right)=\left\{\pm1;\pm13\right\}\)
Xét từng trường hợp :
TH1 : \(\hept{\begin{cases}2+y=1\\3x-1=13\end{cases}}\Leftrightarrow\hept{\begin{cases}y=-1\\x=\frac{14}{3}\end{cases}}\)
TH2:\(\hept{\begin{cases}2+y=13\\3x-1=1\end{cases}\Leftrightarrow\hept{\begin{cases}y=11\\x=\frac{2}{3}\end{cases}}}\)
TH3:\(\hept{\begin{cases}2+y=-1\\3x-1=-13\end{cases}\Leftrightarrow\hept{\begin{cases}y=-3\\x=-4\end{cases}}}\)
TH4:\(\hept{\begin{cases}2+y=-13\\3x-1=-1\end{cases}}\Leftrightarrow\hept{\begin{cases}y=-15\\x=0\end{cases}}\)
Vậy................
/hok chắc/
~ học tốt~