\(4xy-3x+2y=15\)
\(\Leftrightarrow x\left(4y-3\right)+2y=15\)
\(\Leftrightarrow2x\left(4y-3\right)+4y=30\)
\(\Leftrightarrow2x\left(4y-3\right)+4y-3=27\)
\(\Leftrightarrow\left(2x+1\right)\left(4x-3\right)=27\)
Ta có bảng sau:
| 2x + 1 | 27 | 1 | -1 | -27 | 3 | 9 | -3 | -9 |
| 4y - 3 | 1 | 27 | -27 | -1 | 9 | 3 | -9 | -3 |
| x | 13 | 0 | -1 | -14 | 1 | 4 | -2 | -5 |
| y | 1 | \(\dfrac{15}{2}\) | -6 | \(\dfrac{1}{2}\) | 3 | \(\dfrac{3}{2}\) | \(-\dfrac{3}{2}\) | 0 |
Vậy: \(\left(x;y\right)=\left\{\left(13;1\right);\left(-1;-6\right);\left(1;3\right);\left(-5;0\right)\right\}\)
4xy - 3x + 2y = 15
(4xy + 2y) - 3x = 15
2y(2x + 1) - 3x = 15
4y(2x + 1) - 6x = 30
4y(2x + 1) - 6x - 3 = 30 - 3
4y(2x + 1) - 3(2x + 1) = 27
(2x + 1)(4y - 3) = 27
*) TH1: 2x + 1 = -27; 4y - 3 = -1
+) 2x + 1 = -27
2x = -28
x = -14
+) 4y - 3 = -1
4y = 2
y = 1/2 (loại)
*) TH2: 2x + 1 = -9; 4y - 3 = -3
+) 2x + 1 = -9
2x = -10
x = -5
+) 4y - 3 = -3
4y = 0
y = 0
*) TH3: 2x + 1 = -1; 4y - 3 = -27
+) 2x + 1 = -1
2x = -2
x = -1
+) 4y - 3 = -27
4y = -24
y = -6
*) TH4: 2x + 1 = -3; 4y - 3 = -9
+) 2x + 1 = -3
2x = -4
x = -2
+) 4y - 3 = -9
4y = -6
y = -3/2 (loại)
*) TH5: 2x + 1 = 1; 4y - 3 = 27
+) 2x + 1 = 1
2x = 0
x = 0
+) 4y - 3 = 27
4y = 30
y = 15/2 (loại)
*) TH6: 2x + 1 = 3; 4y - 3 = 9
+) 2x + 1 = 3
2x = 2
x = 1
+) 4y - 3 = 9
4y = 12
y = 3
*) TH7: 2x + 1 = 9; 4y - 3 = 3
+) 2x + 1 = 9
2x = 8
x = 4
+) 4y - 3 = 3
4y = 6
y = 3/2 (loại)
*) TH8: 2x + 1 = 27; 4y - 3 = 1
+) 2x + 1 = 27
2x = 26
x = 13
+) 4y - 3 = 1
4y = 4
y = 1
Vậy ta tìm được các cặp giá trị (x; y) thỏa mãn:
(13; 1); (1; 3); (-1; -6); (-5; 0)
