F.2 數學~ 請解答以下聯立二元一次方程(10點)

3x
--- +y=15....................(1)
2

9x-2y=18.....................(2)

From (1)
y = 15 - (3x / 2)..........(3)

Sub. (3) into (2)
9x - 2[15 - (3x / 2)] = 18
9x - 30 + 3x = 18
12x = 48
x = 4 //

Sub. x = 8 into (2)
36 - 2y = 18
2y = 18
y = 9 //

2007-02-05 18:37:12 補充：
sorry~有少少錯漏, 應該是3x--- +y=15....................(1)29x-2y=18.....................(2)From (1)y = 15 - (3x / 2)..........(3)Sub. (3) into (2)9x - 2[15 - (3x / 2)] = 189x - 30 + 3x = 1812x = 48x = 4 //Sub. x = 4 into (2)36 - 2y = 182y = 18y = 9 // 參考資料: me~

2007-02-05 18:46:49 補充：
我的計法係跟足題目要求: 代入消元法, 而不是加減消元法

2007-02-05 18:57:19 補充：
計呢題, 除左將y變做subject, 再substitute y, 另一計法就係將x轉做subject, 計法如下:3x--- +y=15....................(1)29x-2y=18.....................(2)From (1)3x + 2y = 303x = 30 - 2yx = (30 - 2y) / 3...........(3)

2007-02-05 18:57:38 補充：
Sub. (3) into (2), 9[ (30 - 2y) / 3 ] - 2y = 183( 30-2y ) - 2y = 1890 - 6y = 188y = 72y = 9 // Sub. y = 9 into (3)x = 12 / 3x = 4 //

3x
--- +y=15........1
2

9x-2y=18........2

改1:

3x
--- +y=15
2

3x
--- =15-y
2

3x=2(15-y)

x= 30-2y/3........3

代3入2:

9x-2y=18


9(30-2y/3)-2y=18


把3和9約

3(30-2y)-2y=18

90-6y-2y=18

90-8y=18

-8y=18-90

-8y= -72

-8y/-8=-72/-8

y=9

把y=9代入1

3x
--- +9=15
2

3x
--- =15-9
2

3x
--- =6
2

3x=6X2

3x=12

x=12/3

x=4

所以x=4 , y=9

/=分綫

(3x/2)+y=15
⇒y=15-(3x/2)

所以、9x-2y=18
変成
2x-2[15-(3x/2)]=18
2x-[30-(6x/2)]=18
2x-[30-3x]=18
2x-30+3x=18
5x-30=18
5x=18+30
5x=48
x=48/5

x=48/5的話、
y=15-(3x/2)
y=15-[3(48/5)/2]
y=15-[(148/5)/2]
y=15-(148/10)
y=(150/10)-(148/10)
y=2/10

所以,x=48/5;y=2/10

2007-02-05 18:50:04 補充：
改正：(3x/2) y=15⇒y=15-(3x/2)所以、9x-2y=18変成9x-2[15-(3x/2)]=189x-[30-(6x/2)]=189x-[30-3x]=189x-30 3x=1812x-30=1812x=18 3012x=48x=48/12x=4x=4的話、y=15-(3x/2)y=15-[3(4)/2]y=15-[12/2]y=15-6y=9所以,x=4;y=9

將第(1)式全式x2:
2(3x/2+y)=15x2
3x+2y=30------(3)

跟住(3)+(2):
12x=48,
x=4----(4)


將(4)代入(3)
3(4)+2y=30
2y=30-12
y=18/2
y=9

x = 4
y = 9