MathsF.2聯立方程.

1.
x - (y/2) = (x/2) + (y/4) = 2

x - (y/2) = 2 ...... [1]
(x/2) + (y/4) = 2 ...... [2]

[1] * 2 :
2x - y = 4 ...... [3]

[2] * 4 :
2x + y = 8 ...... [4]

[3] + [4] :
4x = 12
x = 3

把 x = 3 代入 [3] 式 :
2*3 - y = 4
y = 2

答案：x = 1, y = 2


2.
4x - 2y = 2(x + y) + y = 5

4x - 2y = 5 ...... [1]
2(x + y) + y = 5 ...... [2]

由 [2] :
2x + 2y + y = 5
2x + 3y = 5
4x + 6y = 10 ...... [3]

[3] - [1] :
8y = 5
y = 5/8

把 y = 5/8 代入 [1] 中 :
4x - 2*(5/8) = 5
4x = 25/4
x = 25/16

答案： x = 25/16, y = 5/8

2011-11-20 02:10:38 補充：
第一題計算正確，但最後卻抄錯了答案。
答案應是 x = 3, y = 2

1. x-(y/2)= 2 -----1
(x/2)+(y/4)=2 -----2

from 1
x-y/2=2
2x-y=4
2x= 4+y-----3

from2
x/2+y/4=8
2x+y=8-----4
sub 3 into 4
4+y+y=8
2y=4
y =2
2x=4+y
2x=4+2
x=3



24x-2y=5--------1
2(x+y)+y=5-------2

from 1
24x-2y=5
12x-y=2.5
y=12x-2.5-----3

from 2
2(x+y)+y=5
2x+3y =5------4

sub 3 into 4
2x+3(12x-2.5)=5
2x+36x-7.5=5
38x=12.5
x = 25/76
y=12x-2.5
y=12*25/76-2.5
y=55/38