~聯立方程~

2007-01-03 12:37 am
求下列聯立方程的解。

Q1) y = x
    2x - y = 3

Q2) y = 5x
    9x - y = 4

Q3) x = 2y
    x + 7y = 27

Q4) y = x + 1
    y + 2x = 16

回答 (2)

2007-01-04 2:23 am
✔ 最佳答案
1)y = x(i)
2x - y = 3(ii)

Substitute (i) into (ii)

2x-x=3
x=3

Substitute x=3 into (i)

y=3
-------------------------------------------------------------------------------------------------------
2)y = 5x(i)
9x - y = 4(ii)

Substitute (i) into (ii)

9x-5x=4
4x=4
x=4/4
x=1

Substitute x=1 into (i)

y=5 x 1
y=5
-------------------------------------------------------------------------------------------------------
3)x = 2y(i)
x + 7y = 27(ii)

Substitute (i) into (ii)

2y+7y=27
9y=27
y=27/9
y=3

Substitute y=3 into (i)

x=2 x 3
x=6
-------------------------------------------------------------------------------------------------------
4)y = x + 1(i)
y + 2x = 16(ii)

Substitute (i) into (ii)

x+1+2x=16
3x+1=16
3x=16-1
3x=15
x=15/3
x=5

Substitute x=5 into (i)

y=5+1
y=6
=========================================================
Vocabularies
1)Simultaneous Linear Equation=聯立方程
1)Substitute ... into ...=代 ... 入 ...
2)From ... =從 ...
參考: 數學能手Me
2007-01-03 1:20 am
Q1) Put y=x into 2x-y=3
2x-x=3
x=3
Then y=x=3

Q2)Put y=5x into 9x-y=4
9x-5x=4
4x=4
x=1
Put x=1 into y=5x
y=5(1)=5


Q3) Put x=2y into x+7y=27
2y+7y=27
9y=27
y=3
Put y=3 into x=2y
x=2(3)=6

Q4)Put y=x+1 into y+2x=16
x+1+2x=16
3x=15
x=5
put x=5 into y=x+1
y=5+1=6

Hopes can help u
參考: myself


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