Ta có: 2xy + y = 18 - 2x
=> 2xy + y - 18 + 2x = 0
=> y(2x + 1) + (2x + 1) = 19
=> (y + 1)(2x + 1) = 19
=> y + 1; 2x + 1 \(\in\)Ư(19) = {1; -1; 19; -19}
lập bảng :
2x + 1 | 1 | -1 | 19 | -19 |
y + 1 | 19 | -19 | 1 | -1 |
x | 0 | -1 | 9 | -10 |
y | 18 | -20 | 0 | -2 |
Vậy ...
\(2xy+y=18-2x\)
\(\Leftrightarrow2xy+2x+y+1=17\)
\(\Leftrightarrow2xy+2x+\left(y+1\right)=17\)
\(\Leftrightarrow2x\left(y+1\right)+\left(y+1\right)=17\)
\(\Leftrightarrow\left(y+1\right)\left(2x+1\right)=17\)
\(\Rightarrow\left(y+1\right)\)và \(\left(2x+1\right)\inƯ\left(17\right)=(\pm1:\pm17)\)
Lập Bảng
2x+1 | 1 | 17 | -1 | -17 |
y+1 | 17 | 1 | -17 | -1 |
x | 0 | 8 | -1 | -8 |
y | 16 | 0 | -18 | -2 |