數學解分數、小數聯立方程式

1.
(5x - 2y + 4) / 3 = 0.5 (3x + 4y - 7) -----(1)
0.25 (4x + 5y - 2) = (x + y + 5) / 2 ---------(2)
(1)X6: 2 (5x - 2y + 4) = 3 (3x + 4y - 7)
10x - 4y + 8 = 9x + 12y - 21
x - 16y + 29 = 0 ------(3)
(2)X4: 4x + 5y - 2 = 2 (x + y + 5)
4x + 5y - 2 = 2x + 2y + 10
2x + 3y -12 = 0 ------(4)
(4) - (3)X2: 2x + 3y -12 - 2 (x - 16y +29) = 0
2x + 3y -12 - 2x + 32y - 58 = 0
35y -70 = 0
35y = 70
y = 2 ----(5)
代(5)入(3), x - 16 (2) + 29 = 0
x = 3

2.
(4x - 3y + 5) / 2 = (2x - y + 12) / 3 -----(1)
0.2 (x - 7y) = 0.5 (-3x + 5y - 1) ----------(2)
(1)X6: 3 (4x - 3y + 5) = 2 (2x - y + 12)
12x - 9y + 15 = 4x - 2y + 24
8x - 7y - 9 = 0 -------(3)
(2)X10: 2 (x - 7y) = 5 (-3x + 5y - 1)
2x - 14y = -15x + 25y - 5
17x - 39y + 5 = 0-----(4)
(3)X17 - (4)X8: 17 (8x - 7y - 9) - 8 (17x - 39y + 5) = 0
-119y - 153 + 312y - 40 = 0
193y - 193 = 0
y = 1 -----(5)
代(5)入(3), 8x - 7 (1) - 9 = 0
8x - 16 = 0
8x = 16
x = 2

3.
-3x + 7y = 2 (x + 5y) + 11 -------(1)
3 (2x + 5y) = x + 6 (2y - 1) ------(2)
由(1), -3x + 7y = 2 (x + 5y) + 11
-3x + 7y = 2x + 10y + 11
5x + 3y + 11 = 0 -----(3)
由(2), 3 (2x + 5y) = x + 6 (2y - 1)
6x + 15y = x + 12y - 6
5x + 3y + 6 = 0 -------(4)
(3) - (4): 11 - 6 = 0 (這個不可能11 - 6 應該是 5)
所以, 這組聯立方程是無解

4.
(3x + 2y) / 5 = (x - 3y + 1) / 2 -----(1)
0.6 (2x + 3y) = x - 2y + 1 -----------(2)
(1)X10: 2 (3x + 2y) = 5 (x - 3y + 1)
6x + 4y = 5x - 15y + 5
x + 19y - 5 = 0 -----(3)
(2)X5: 3 (2x + 3y) = 5 (x - 2y + 1)
6x + 9y = 5x - 10y + 5
x + 19y - 5 = 0 -----(4)
因為(3) 和 (4) 是一樣, 即是原本(1) 和 (2) 是一樣,
也是說, 2條方程所代表的直線是重疊,
所以, 這組聯立方程是無限解



2014-08-12 17:28:22 補充：
麻辣,

=|1 -16 29 1| (這行的數字即是1是怎來?)
.|2 .3 -12 2| (這行的數字即是2是怎來?)

=(3+32,192-87,58+12) (你這行做了什麼運算?)

=(35,105,70)

=(105,70)/35

=(3,2)

2014-08-13 07:48:14 補充：
麻辣,
我記起來了, 這個方法叫Cramer's Rule, 不過麻辣知識長做法跟原來的有少少不同,
所以一開始認不出來,
下次用其他方法時, 希望麻辣知識長也提供一下方法名稱,
使大家都能知道麻辣知識長在做什麼

不知道你有沒有興趣看看
http://qoozoo04480609.pixnet.net/blog








歮吅犇靐品叒

2014-08-13 06:32:48 補充：
到下面的網址看看吧

▶▶http://*****