二元一次方程(1)

2007-10-06 10:12 pm
1.已知兩個數的和是123.而差是31.求這兩個數
2.已知2個蘋果和3個橙的售價是$13.而4個蘋果和1個橙的售價是$11.求每個蘋果和每個橙的售價??
3.已知小明比小美重4kg.他們的總重量是102kg..他們的重量分別是??
4.已知小如有$5及$2硬幣.若小如有35個硬幣.而總值是$130.問小如有$5及$2硬幣各多少?

回答 (3)

2007-10-06 10:43 pm
✔ 最佳答案
1. 設其中一個數為x , 另一個數為y
x+y=123.......1
x-y=31
x=31+y....2
把2代入1
31+y+y=123
2y=92
y=46
把y=46代入2
x=31+46
=77
∴這兩個數分別是77,46

2 .設每個蘋果和每個橙的售價分別為$x,$y
2x+3y=13.........1
4x+y=11
y=11-4x.......2
把2代入1
2x+3(11-4x)=13
2x+33-12x=13
10x=20
x=2
把x=2代入2
y=11-4(2)
=3
∴每個蘋果和每個橙的售價分別是$2,$3

3. 設小美和小明的重量分別為x kg, y kg
y-x=4
y=4+x........1
x+y=102........2
把1代入2
x+4+x=102
2x=98
x=49
把y=49代入1
y=4+49
=53
∴小美和小明的重量分別是49kg, 53kg

4. 設$5及$2硬幣的數量分別為x, y
x+y=35
x=35-y.........1
5x+2y=130..........2
把1代入2
5(35-y)+2y=130
175-5y+2y=130
3y=45
y=15
把y=15代入1
x=35-15
=20
∴$5及$2硬幣的數量分別是20,15
2007-10-06 10:40 pm
未知數: a , a +31
a+31+a = 123
2a = 92
a = 46
所以 2個數 就是 46 , 77 ... ( 77點黎?? a=46 46+31 )

2. 未知數 : x= apple , y = orange
2x +3y = 13
4X + Y = 11 2條數一樣的
y= 11-4x
2X + 3(11-4x) = 13
2X+33-12x = 13
- 10X = -20X
X = 2
第1條 2(2)+ 3y = 13
3y = 9
y = 3
所以 apple = $2 orange = $3

未知數 : a , a+4
3 . a+a+4 = 102
2a = 98
a = 49
所以 分別係 49 , 53 ...

2007-10-06 14:54:17 補充:
4. 未知數$5 = x $2x= yx y=35x=35-y5x 2y=1305(35-y) 2y=130 - 5y 2y = -45 -3y= - 45y=15x=35-15 ( 第1條式) x=20所以 $5 有 20個 $2 有 15

2007-10-06 14:56:19 補充:
4. 未知數$5 = x $2= yx y=35x=35-y5x 2y=1305(35-y) 2y=130- 5y 2y = -45 -3y= - 45y=15x=35-15 ( 第1條式)x=20所以 $5 有 20個 $2 有 15個 之前 打小左野 sorry ..
參考: me
2007-10-06 10:29 pm
1. X+Y =123 ------------------1
X-Y=31 -----------------------2

from 2 , X = 31+Y
therefore 31+Y+Y = 123, 2Y= 92, Y= 46, X=77.


2. X = price of apple, Y= price of orange
2X+3Y =13------------------- 1
4X+Y =11--------------------- 2

from 2, Y=11-4X
therefore 2X+3(11-4X) = 13, 2X+33-12X= 13 , 20=10X, X=2, Y=3.

2007-10-06 14:35:29 補充:
3. 小明=X, 小美=Y, therefore X-Y=4---------------------------- 1 and X+Y =102 ----------------------------- 2from 1, X = 4+Y, therefore 4+Y+Y =102, Y=49, X= 53

2007-10-06 14:35:51 補充:
4. let X=number of $5, let Y=number of $2 X+Y =35--------------------------- 1 5X+2Y =130----------------------- 2use the above 3 example, try try this one by yourself la


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