Question

解一个方程,不是应用题!是计算题!

方程组:8359x-1641y=28359
1641x-8359y=21641
要求:要用简便方法来计算,并且要有过程.

Answer 1

8359x-1641y=28359......... ①
1641x-8359y=21641......... ②

解：将两个方程相加，得
1641(x-y)+8359(x-y)=50000
(1641+8359)(x-y)=50000
10000(x-y)=50000
x-y=5
由x-y=5，得x=y+5，并代入①，得
8359(y+5)-1641y=28359
6718y=-13436
y=-2
将y=-2代入x-y=5，得
x=3
所以
x=3
y=-2

Answer 2

8359x-1641y=28359 ...(1)
1641x-8359y=21641 ...(2)

(1)+(2)
10000x -10000y =50000
x -y =5 ...(3)

(1)-(2)
6718x +6718y =6718
x +y =1 ...(4)

(3)+(4)
2x =6
x = 3

(3)-(4)
-2y =4
y = -2

所以，x=3,y=-2.

Answer 3

(1)+(2)
10000x-10000y=50000
x-y=5 (3)
(1)-(2)
6718x+6718y=6718
x+y=1 (4)
解(3)、(4)式，得
x=3
y=-2

Answer 4

两式相加为：1000（x-y)=50000 x-y=5
两式相减为：6718（x+y)=6718 x+y=1
解得：x=3 y=-2

Answer 5

两式相减：
6718x+6718y=6718 得 x+y=1
两式相加：
10000x-10000y=50000得x-y=5
所以，x=3,y=-2

Answer 6

8359x+1641x-1641y-8359y=28359+21641
10000x-10000y=50000
x-y=5