[數學]加減消元法

1.
5x - y = 0 ...... [1]
5x + 2y = -15 ...... [2]

[2] - [1] :
3y = -15
y = -5

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

[2] + [3] :
15x = -15
x = -1


2.
x + 6y = 2 ...... [1]
5x - 6y = 46 ...... [2]

[1] + [2] :
6x = 48
x = 8

[1] * 5 :
5x + 30y = 10 ...... [3]

[3] - [2] :
36y = -36
y = -1


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

[1] x 2 :
10x + 2y = 6 ...... [3]

[2] + [3] :
11x = 11
x = 1


[2] * 5 :
5x - 10y = 25 ...... [4]

[1] - [4] :
11y = -22
y = -2


4.
5x + 8y = 14 ...... [1]
3x - 2y = -12 ...... [2]

[2] * 4 :
12x - 8y = -48 ...... [3]

[1] + [3] :
17x = -34
x = -2

[1] * 3 :
15x + 24y = 42 ...... [4]

[2] * 5 :
15x - 10y = -60 ...... [5]

[4] - [5] :
34y = 102
y = 3


5.
2y + 3x +4 = 0 ...... [1]
2x - 3y + 7 = 0 ...... [2]

[1] * 2 :
6x + 4y = - 8 ...... [3]

[2] * 3 :
6x - 9y = -21 ...... [4]

[3] - [4] :
13y = 13
y = 1

[1] * 3 :
9x + 6y = -12 ...... [5]

[2] * 2 :
4x - 6y = -14 ...... [6]

[5] + [6] :
13x = -26
x = -2

1

5x - y = 0
5x + 2y = -15

5x + 2y = -15
5x - y = 0..................兩式相減。

3y= -15
y= -5

y= -5
x= -1


2.
x + 6y = 2
5x - 6y =46

x + 6y = 2
5x - 6y =46............兩式相加。

6x=48
x=8

x=8
y= -1


3.
5x + y =3
x - 2y = 5

10x + 2y =6.................X2
x - 2y = 5

10x + 2y =6
x - 2y = 5............兩式相加。

11x=11
x=1

x=1
y= -2


4.
5x + 8y = 14
3x - 2y = -12

5x + 8y = 14
12x - 8y = -48...........X4

5x + 8y = 14
12x - 8y = -48...........兩式相加。

17x= -34
x= -2

x= -2
y= 3


5.
2y + 3x +4 = 0
2x - 3y + 7 = 0

2y + 3x +4 = 0
- 3y +2x + 7 = 0

6y + 9x +12 = 0..................X3
- 6y +4x + 14 = 0 ............X2

6y + 9x +12 = 0
- 6y +4x + 14 = 0....................兩式相加。

13x+26=0
x=-2

x=-2
y=1
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我個人睇法咁計係簡潔既，不過睇唔慣未必明，所以加左解釋，現實係無必要既。

當你求到一個未知數，代入去求另一個未知數，你唔代入另一條式求證，你未免太過唔小心勒。