解聯立方程

2009-10-06 3:58 am
1.) x/3 - y/3=x/2+y/6=8

2.)
26x + 3y=- 4
x-2/5=1-y/4

3.)
x/2 - y/4 =2
2x/5 + y/6 =6

4.)
4x - 3y=5
2x+y= - 5

5.)
4x+3y=20
x-2y= - 6

6.)
p+1/q =2/3
p - 2/q+3 =3/7

7.)
1/x +2/y=5
3/x - 1/y=1

回答 (1)

2009-10-07 6:44 am
✔ 最佳答案
(1) x/3 – y/3 = 8 … (1)
x/2 + y/6 = 8 … (2)
(1) * 3 => x – y = 24 …(3)
(2) * 6 => 3x + y = 48 … (4)
(3) + (4) => 4x = 72
x = 18
Sub into (1), 18 – y = 24
y = -6
(2) 26x + 3y = -4 … (1)
(x – 2)/5 = (1 – y)/4 … (2)
(2)*12 => 2.4x – 4.8 = 3 – 3y
2.4x + 3y = 7.8 … (3)
(1) – (3) => 23.6x = -11.8
x = -0.5
Sub into (1)=> -13 + 3y = -4
y = 3
(3) x/2 – y/4 = 2 …(1)
2x/5 + y/6 = 6 … (2)
(1)*4 => 2x – y = 8 … (3)
(2)*6 => 2.4x + y = 36 … (4)
(3) + (4) => 4.4x = 44
x = 10
Sub into (1) => 5 – y/4 = 2
y = 12
(4) 4x – 3y = 5 … (1)
2x + y = -5 … (2)
(2) * 3 => 6x + 3y = -15 … (3)
(1) + (3) => 10x = -10
x = -1
sub into (2), -2 + y = -5
y = -3
(5) 4x + 3y = 20 … (1)
x – 2y = -6 … (2)
(2) * 4 => 4x – 8y = -24 … (3)
(1) – (3) => 11y = 44
y = 4
Sub into (2), x – 8 = -6
x = 2
(6) (p + 1)/q = 2/3 … (1)
(p – 2)/(q + 3) = 3/7 … (2)
(1) => 3p + 3 = 2q
9p + 9 = 6q … (3)
(2) => 7p – 14 = 3q + 9
14p – 28 = 6q + 18
14p – 46 = 6q … (4)
(3) – (4) => -5p + 55 = 0
p = 11
Sub into (3), 99 + 9 = 6q
q = 18
(7) 1/x + 2/y = 5 … (1)
3/x – 1/y = 1 … (2)
(2)*2 => 6/x – 2/y = 2… (3)
(1) + (3) => 7/x = 7
x = 1
Sub into (1) => 1 + 2/y = 5
y = 1/2


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