中二數學聯立方程

2a + 5b = 47ab........(1)

4b = 3a + 10ab........(2)

(1) * 10 - (2) * 47

10(2a + 5b) - 47 * 4b = 10 * 47ab - 47 * (3a + 10b)

20a + 50b - 188b = 470ab - 141a - 470ab

20a - 138b = -141a

141a + 20a = 138b

161a = 138b

a = 138b / 161 = 6b / 7.............(3)

Sub (3) into (1), 2(6b / 7) + 5b = 47b(6b / 7)

12b / 7 + 5b = 282b^2 / 7

7 * [12b / 7 + 5b] = 7 * [282b^2 / 7]

12b + 35b = 282b^2

282b^2 - 47b = 0

47b(6b - 1) = 0

b = 0 or 1 / 6.

When b = 0, a = 6(0) / 7 = 0; when b = 1 / 6, a = 6(1 / 6) / 7 = 1 / 7.