MATHS!! simultaneous equation

👨🏻‍🏫 學術台數學

[匿名]

2009-11-01 1:25 am

請問點樣去分辨infinite equation同正常既equation
姐係
x+y=2
x/2-y/3=1
同
2x-1=3(1-y)
3(3-4y)=8x-7
有咩分別?

更新1:

同埋inconsistent equation又係點分辨

更新2:

carA and carB are 120km apart.If they move towards each other,they will meet in 1hr.If they move in the same direction,carA will catch up carB in 5hrs.Find the speeds of carA and carB(assume the speeds of both cars do not change)

回答 (2)

用戶9112

2009-11-01 3:02 am

✔ 最佳答案

x + y = 2 ... (1)
x/2 - y/3 = 1 ... (2)
(1) * 2 => 2x + 2y = 4 ... (3)
(2) => 3x - 2y = 6 ... (4)
(3) + (4) => 5x = 10 => x = 2 => y = 0
明顯這對Equation 只有一組解(normal equation)
2x - 1 = 3(1 - y) ... (1)
3(3 - 4y) = 8x - 7 ... (2)
(1) => 2x - 1 = 3 - 3y
2x + 3y = 4 ... (3)
(2) => 9 - 12y = 8x - 7
8x + 12y = 16
2x + 3y = 4 ... (4)
明顯(3)和(4)是一樣的,結果是無法找到唯一的解,但有無窮的解(infinite equation) 如:x = 2, y = 0; x = -1, y = 2, 等等
另如
2x - 2 = 3(1 - y) ... (1)
3(3 - 4y) = 8x - 7 ... (2)
(1) => 2x + 3y = 5 ... (3)
(2) => 2x + 3y = 4 ... (4)
(3)和(4)明顯互相矛盾(inconsistent equation),是無沒找到任何的解的.

2009-11-01 00:35:02 補充：
Let speeds be A km/hr and B km/hr
(A + B) * 1 = 120 ... (1)
(B - A) * 5 = 120
B - A = 24 ... (2)
(1) + (2) => 2B = 144 => B= 72
Sub into(1), A + 72 = 120 => A = 48
Speed of car A is 48km/hr and of car B 72 km/hr

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石石

2009-11-01 3:17 am

the simultaneous equation has infinite many solutions <=> it is a inconsistent equation <=> the two equations have the same slope.

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