? 發問於 科學及數學數學 · 1 十年 前

# F.3. MATHS EQUATION

F.3 Chapter 1

Linear Equation in Two Unknowns

Solve the following equation

1) {2/x - 1/y = 21 ; -5/y + 1/x =9

2) { 2(x-3)+y=0 ; (x-1)/2 - 3(y-1)=x

3) { 3(2x-4y)+22 = -2y ; (4x-2y)/3 = y-2x

4) { 1-0.3(5-2)=1/5(t+1) ; (S-3)/4 = [(4t+9)/20] -1.5

5) { (x+1)/2 + (y+3)/4 = 5; (x+2)/3 - (2y+3)/4 =2

THZ

### 2 個解答

• 1 十年 前
最佳解答

1) {2/x - 1/y = 21 ; -5/y + 1/x =9

2/x – 1/y = 21 ___(1)

-5/y + 1/x = 9 ___(2)

(2)式乘2得

-10/y + 2/x = 18 ___(3)

(1)式減(3)式

9/y = 3

9 = 3y

y = 3

代入(1)

2/x – 1/3 = 21

2/x = 21+1/3 = 64/3

1/x = 32/3

x = 3/32

2) { 2(x-3)+y=0 ; (x-1)/2 - 3(y-1)=x

2(x-3)+y=0 ___(1)

(x-1)/2 - 3(y-1)=x ___(2)

由(1)式

2x – 6 + y = 0

y = 6 – 2x ___(3)

(3)式代入(2)式

(x-1)/2 - 3(y-1)=x

(x-1)/2 - 3(6 – 2x -1)=x 全式乘2

(x – 1) – 6(5 – 2x) = 2x

x – 1 – 30 + 12x = 2x

11x – 31 = 0

x = 31/11 代入(3)式

y = 6 – 2x

= 6 – 2(31/11)

= 6 – 62/11

y = 4/11

3) { 3(2x-4y)+22 = -2y ; (4x-2y)/3 = y-2x

3(2x-4y)+22 = -2y ___(1)

(4x-2y)/3 = y-2x ___(2)

由(1)

6x – 12y + 22 = -2y

6x – 10y + 22 = 0 ___(3)

由(2)式乘3

4x – 2y = 3y – 6x

10x = 5y

y = 2x 代入(3)

6x – 10y + 22 = 0

6x – 10(2x) + 22 = 0

6x – 20x + 22 = 0

- 14x = -22

x = 22/7 代入

y = 2x

y = 2(22/7)

y = 44/7

4) { 1-0.3(5-2)=1/5(t+1) ; (S-3)/4 = [(4t+9)/20] -1.5

1-0.3(5-2)=1/5(t+1) ___(1)

(S-3)/4 = [(4t+9)/20] -1.5 ___(2)

由(1)

1 – 0.9 = 1/5(t+1)

0.1 = 1/5(t+1) 全式 10(t+1)

t + 1 = 2

t = 3 代入(2)式

(S-3)/4 = [(4t+9)/20] -1.5

(S-3)/4 = [(4(3)+9)/20] -1.5

(S-3)/4 = [(12+9)/20] -1.5

(S-3)/4 = 21/20 -1.5

(S-3)/4 = 1.05 -1.5

(S-3)/4 = -0.45

S – 3 = -1.8

S = 1.2

5) { (x+1)/2 + (y+3)/4 = 5; (x+2)/3 - (2y+3)/4 =2

(x+1)/2 + (y+3)/4 = 5 ___(1)

(x+2)/3 - (2y+3)/4 =2 ___(2)

(1)式乘4

2(x+1) + (y+3) = 20

2x + 2 + y + 3 = 20

y = 15 – 2x 代入(2)式

(x+2)/3 - (2y+3)/4 =2

(x+2)/3 - (2(15 – 2x )+3)/4 =2 全式乘12

4(x+2) - 3(2(15 – 2x )+3) =24

4x + 8 – 6(15 – 2x) – 9 = 24

4x + 8 – 90 + 12x – 9 = 24

16x = 115

x = 115/16 代入

y = 15 – 2x

y = 15 – 2(115/16)

y = 15 – (115/8)

y =5/8

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• 1 十年 前

1) 2/x - 1/y = 21.......(1)

-5/y + 1/x =9.........(2)

(2)乘2=-10/y+2/x=18........(3)

(3)-(2)=-10/y+2/x-(2/x-1/y)=9-21

11/y=-12

y=-11/12

put y=-11/12 into(1),

2/x-1/y=21

2/x-1乘-12/11=21

x=22/219

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