2條中三數學題(代入法)

1.
(1/3)x + (2/5)y = -7 ...... (1)
(1/9)x + (3/5)y = 7 ...... (2)

(1) 乘以 15:
5x + 6y = -105 ...... (3)

(2) 乘以 45:
5x + 27y = 315
5x = 315 - 27y ...... (4)

(4) 代入 (3):
(315 - 27y) + 6y = -105
315 - 21y = -105
-21y = -420
y = 20

y = 20 代入 (4):
5x = 315 - 27(20)
5x = -225
x = -45

答：x = -45, y = 20



2.
0.7x + (2/3)y = 1 ...... (1)
0.6x + (1/9)y = 1 ...... (2)

(2) 乘以 9:
5.4x + y = 9
y = 9 - 5.4x ...... (3)

(3) 代入 (1):
0.7x + (2/3)(9 - 5.4y) = 1
全式乘以 3:
2.1x + 2(9 - 5.4x) = 3
2.1x + 18 - 10.8x = 3
-8.7x = -15
x = 50/29

x = 50/29 代入 (3):
y = 9 - 5.4(50/29)
y = 9 - 270/29
y = -9/29

答： x = 50/29, y = -9/29

書的答案錯誤。
將書的答案代入 (2):
左方 = 0.6(10) + (1/9)(-9) = 5 ≠ 右方

把我的答案代入 (1):
左方 = 0.7(50/29) + (2/3)(-9/29) = (35/29) - (6/29) = 1 = 右方

把我的答案代入(2):
左方 = 0.6(50/29) + (1/9)(-9/29) = (30/29) - (1/29) = 1 = 右方

所以我的答案是正確的。

你將書的答案代入第二條式：
左邊 = 0.6(10) + (1/9)(-9) = 5
右邊 = 1
本書的答案錯。但連這般簡單的驗算也不做，我只有刪除答案。