數學直線問題T-T 唔識解

[匿名]

2010-01-31 11:43 pm

諗左好耐...但係又唔知肯唔肯定..好心人請幫幫手..唔該晒

判斷下列各對直線的位置關係....如果相交....求出交點坐標

(1)
L1:2x-3y=7 L2:4x+2y=1

(2)
L1:2x-6y+4=0 L2: y= 3份之x + 3份之2

(3)
L1: (根號2 - 1)x+y=3 L2: x+(根號2 + 1)y=2

thank you!!!!!

更新1:

thank you!!!!!

回答 (1)

用戶2053

2010-02-01 3:46 am

✔ 最佳答案

1)L1:2x-3y=7 .....(1)
L2:4x+2y=1.....(2)
(2)-(1)*2 :
2y - 2(-3y) = 1 - 7*2
8y = - 13
y = -13/8 , 代入(1)
2x - 3(-13/8) = 7
2x = 7 - 39/8
x = 17/16
L1 L2 交於 (17/16 , -13/8)
2)
L1:2x-6y+4=0 , 斜率 = -2/(-6) = 1/3
L2: y= (1/3)x + 2/3 , 斜率 = 1/3
L1 // L2
3)L1: (√2 - 1)x+y=3 , 斜率 = - (√2 - 1)/1 = 1 - √2
L2: x+(√2 + 1)y=2 , 斜率 = - 1 / (√2 + 1) = - 1(√2 - 1) / [(√2 + 1) (√2 - 1) ]
= 1 - √2
L1 // L2

2010-01-31 21:26:03 補充：
You're welcome !!!!

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