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.