解答

3.
x + y = 3xy
x - y = xy

2x = 4xy, 2y = 1, => y = 1/2
2y = 2xy, x = 1

4.
3(2y - 1) + 4(x - 3) = 7(x - 3)(2y - 1)
4(2y - 1) - 3(x - 3) = (x - 3)(2y - 1)

4x + 6y - 15 = 14xy - 7x - 42y + 21
3x - 8y - 5 = -2xy + x + 6y - 3

11x + 48y = 14xy + 36
2x - 14y = -2xy + 2

11x + 48y = 14xy + 36
14x - 98y = 14 - 14xy

25x - 50y = 50, x - 2y = 2, x = 2y + 2

2x - 14y = -2xy + 2
x - 7y = -xy + 1 = 1 - xy
2y + 2 - 7y = 1 - y(2y + 2)
2y^2 - 3y + 1 = 0
(y - 1)(2y - 1) = 0
y = 1 或 1/2 => x = 4 或 3

即 (x, y) = (4, 1) 或 (3, 1/2)
但是 (3, 1/2) 代入後分母 = 0 => 故不合

=> x = 4, y = 1

訪客

第三題、
為什麼2y=1😅😅

Balm of Gilead

2x = 4xy
可以理解成
2x·1 = 2x·2y
兩邊同除以 2x
1 = 2y

訪客

會了會了!非常的感謝你!

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