Ta có : xy+3x-7y=23
<=> x(y+3)-7y-21=2
<=> x(y+3)-7(y+3)=2
<=> (x-7)(y+3)=2
Đến đó tự làm
\(xy+3x-7y=23\)
\(\Rightarrow x\left(y+3\right)-7y-21=2\)
\(\Rightarrow x\left(y+3\right)-7y-7.3=2\)
\(\Rightarrow x\left(y+3\right)-7\left(y+3\right)=2\)
\(\Rightarrow\left(x-7\right)\left(y+3\right)=2\)
\(\Rightarrow\left(x-7\right)\left(y+3\right)=\pm1.\pm2\)
\(\Rightarrow\orbr{\begin{cases}x-7=\pm1\\y+3=\pm2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=8;x=6\\y=-1;y=-5\end{cases}}\)
\(xy+3x-7y=23\)
\(x\left(y+3\right)-7y=23\)
\(x\left(y+3\right)-7\left(y+3\right)=2\)
\(\left(x-7\right)\left(y+3\right)=2\)
\(\text{Ta có bảng : }\)
| \(x-7\) | \(-2\) | \(-1\) | \(2\) | \(1\) |
| \(y+3\) | \(-1\) | \(-2\) | \(1\) | \(2\) |
| \(x\) | \(5\) | \(6\) | \(9\) | \(8\) |
| \(y\) | \(-4\) | \(-5\) | \(-2\) | \(-1\) |
\(\text{Vậy }\left(x\text{ ; }y\right)=\left(5\text{ ; }-4\right),\left(6\text{ ; }-5\right),\left(9\text{ ; }-2\right),\left(8\text{ ; }-1\right)\)
