Question

[Lạc Chỉ]

Tìm x, y \(\in\)\(ℤ\)biết:

a/ xy + 3x - 7y = 21

b/ xy + 3x - 2y = 11

Answer 1

[ღᏠᎮღ🅼🅸🅽🅷ঔ🅽🅶ụ🆈ঌ__[ᴅʀᴇᴀм тᴇᴀм]__]

\(a)xy+3x-7y=21\)

\(\Leftrightarrow xy+3x-7y-21=0\)

\(\Leftrightarrow\left(xy+3x\right)-\left(7y+21\right)=0\)

\(\Leftrightarrow x\left(y+3\right)-7\left(y+3\right)=0\)

\(\Leftrightarrow\left(y+3\right)\left(x-7\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}y+3=0\\x-7=0\end{cases}\Leftrightarrow\orbr{\begin{cases}y=-3\\x=7\end{cases}}}\)

Answer 2

[ღᏠᎮღ🅼🅸🅽🅷ঔ🅽🅶ụ🆈ঌ__[ᴅʀᴇᴀм тᴇᴀм]__]

\(b)xy+3x-2y=11\)

\(\Leftrightarrow\left(xy+3x\right)-2y=6+5\)

\(\Leftrightarrow x\left(y+3\right)-2y-6=5\)

\(\Leftrightarrow x\left(y+3\right)-\left(2y+6\right)=5\)

\(\Leftrightarrow x\left(y+3\right)-2\left(y+3\right)=5\)

\(\Leftrightarrow\left(y+3\right)\left(x-2\right)=5\Rightarrow\left(y+3\right);\left(x-2\right)\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

Xét các trường hợp :

• \(\hept{\begin{cases}y+3=5\\x-2=1\end{cases}\Leftrightarrow\hept{\begin{cases}y=2\\x=3\end{cases}}}\)
• \(\hept{\begin{cases}y+3=1\\x-2=5\end{cases}}\Leftrightarrow\hept{\begin{cases}y=-2\\x=7\end{cases}}\)
• \(\hept{\begin{cases}y+3=-5\\x-2=-1\end{cases}}\Leftrightarrow\hept{\begin{cases}y=-8\\x=1\end{cases}}\)
• \(\hept{\begin{cases}y+3=-1\\x-2=-5\end{cases}}\Leftrightarrow\hept{\begin{cases}y=-4\\x=-3\end{cases}}\)