? 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

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  • 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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