數學推理(代數)

1. 3a + b = 24 ......... (i)
3b + c = 33 ............. (ii)
3c + a = 23 ............. (iii)
a + b + c + a = 25 ... (iv)
(i) + (ii) + (iii) 得 : 4a + 4b + 4c = 80
所以 : a + b + c = 20
代入 (iv), 得 a = 5
代入 (i), 得 b = 9
代入 (ii), 得 c = 6
所以, a = 5, b = 9, c = 6

2. 3a + b = 13 ........... (i)
3b + c = 20 ............... (ii)
3c + a = 27 ............... (iii)
a + b + c + 10 = 25 ... (iv)
從 (i) 得 b = 13 - 3a ... (v)
從 (ii) 得 c = 20 - 3(13 - 3a)
c = 9a - 19 ................. (vi)
將 (v), (vi) 代入 (iv) 得
a + 13 - 3a + 9a - 19 + 10 = 25
a = 3
代入 (i), 得 b = 4
代入 (ii), 得 c = 8
所以, a = 3, b = 4, c = 8