聯立二元一次方程

2013-07-22 4:12 am
甲.
利用代入消元法解下列聯立二元一次方程。
1. 2x-y=8 2. 4x=37-1 3. 2x-3y=1 4. x+5(y-2)=x+y-4=0
3x-y=6 3x=y-7 3x+4y=10
利用加減消元法解下列聯立二元一次方程。
5. 2x-y=6 6. x+4y=9 7. 2x-5y=-13 8. 2y+x=5 9. 3x-5y=8
2x+3y=2 3x+y=5 x+3y=10 3x-y=8 7x-2y=9
10. 2x=y-1 11. 2(x-1)+7y=3x-2(y-1)=15
3x+2y+3=0

回答 (1)

2013-07-22 5:56 am
✔ 最佳答案
1.
2x - y = 8 ... [1]
3x - y = 6 ... [2]

由 [1] :
-y = 8 - 2x ... [3]

將 [3] 代入 [1] 中:
3x + 8 - 2x = 6
x = -2

將 x = -2 代入 [3] 中:
-y = 8 - 2(-2)
y = -12


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2.
4x = 37 - 1 ... [1]
3x = y - 7 ... [2]

由 [1]:
4x = 36
x = 9

將 y = 9 代入 [2] 中:
3(9) = y - 7
y = 20


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3.
2x - 3y = 1 ... [1]
3x + 4y = 10 ... [2]

由 [1]:
x = (3y + 1)/2 ... [3]

將 [3] 代入 [2] 中:
[3(3y + 1)/2] + 4y = 10
9y + 3 + 8y = 20
17y = 17
y = 1

將 y = 1 代入戋 [3] 中:
x = (3 + 1)/2
x = 2


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4.
x + 5(y - 2) = 0 ... [1]
x + y - 4 = 0 ... [2]

由 [2]:
x = 4 - y ... [3]

將 [3] 代入 [1] 中:
4 - y + 5y - 10 = 0
4y = 6
y = 3/2

將 y = 3/2 代入 [3] 中:
x = 4 - (3/2)
x = 5/2


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5.
2x - y = 6 ... [1]
2x + 3y = 2 ... [2]

[2] - [1]:
4y = -4
y = -1

將 y = -1 代入 [1] 中:
2x - (-1) = 6
x = 5/2


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6.
x + 4y = 9 ... [1]
3x + y = 5 ... [2]

[1] * 3 :
3x + 12y = 27 ... [3]

[3] - [2]:
11y = 22
y = 2

將 y = 2 代入 [2] 中:
3x + 2 = 5
x = 1


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7.
2x - 5y = -13 ... [1]
x + 3y = 10 ... [2]

[2] * 2:
2x + 6y = 20 ... [3]

[3] - [1]:
11y = 33
y = 3

將 y = 3 代入 [2] 中:
x + 3(3) = 10
x = 1


=====
8.
2y + x = 5 ... [1]
3x - y = 8 ... [2]

[1] * 3:
3x + 6y = 15 ... [3]

[3] - [2]:
7y = 7
y = 1

將 y = 1 代入 [1] 中:
2(1) + x = 5
x = 3


=====
9.
3x - 5y = 8 ... [1]
7x - 2y = 9 ... [2]

[1] * 2:
6x - 10y = 16 ... [3]

[2] * 5:
35x - 10y = 45 ... [4]

[4] - [3]:
29x = 29
x = 1

將 x = 1 代入 [1] 中:
3(1) - 5y = 8
y = -1


=====
10.
2x = y - 1 ... [1]
3x + 2y + 3 = 0 ... [2]

[1] * 2:
4x = 2y - 2
4x - 2y + 2 = 0 ... [3]

[2] + [3]:
7x + 5 = 0
x = -5/7

把 x = -5/7 代入 [1] 中:
2(-5/7) = y - 1
y = -3/7


=====
11.
2(x - 1) + 7y = 15 ... [1]
3x - 2(y - 1) = 15 ... [2]

由 [1]:
2x + 7y = 17
6x + 21y = 51 ... [3]

由 [2]:
3x - 2y = 13
6x - 4y = 26 ... [4]

[3] - [4]:
25y = 25
y = 1

把 y = 1 代入 [4] 中:
6x - 4(1) = 26
x = 5

2013-07-29 11:20:47 補充:
2.
題目的 37 應是 3y 之誤。

4x = 3y - 1 ... [1]
3x = y - 7 ... [2]

由 [2]:
y = 3x + 7 ... [3]

將 [3] 代入 [1] 中:
4x = 3(3x + 7) - 1
4x = 9x + 20
5x = -20
x = -4

將 x = -4 代入 [2] 中:
3(-4) = y - 7
y = -5

2013-07-29 11:21:11 補充:
2.
題目的 37 應是 3y 之誤。

4x = 3y - 1 ... [1]
3x = y - 7 ... [2]

由 [2]:
y = 3x + 7 ... [3]

將 [3] 代入 [1] 中:
4x = 3(3x + 7) - 1
4x = 9x + 20
5x = -20
x = -4

將 x = -4 代入 [2] 中:
3(-4) = y - 7
y = -5
參考: 不用客氣, 不用客氣


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