數學推理(代數)

a + b + c + d = 19 ... [1]
2a + b + c = 20 ... [2]
a + b + 2d = 21 ... [3]
2b + c + d = 22 ... [4]

[2] - [1] gives a - d = 1 that is, a = d + 1
[3] - [1] gives d - c = 2 that is, c = d - 2
[4] - [1] gives b - a = 3 that is, b = a + 3 = d + 4

By [1],
(d + 1) + (d + 4) + (d - 2) + d = 19
4d + 3 = 19
4d = 16
d = 4
a = d + 1 = 5
c = d - 2 = 2
b = d + 4 = 8

Therefore, (a, b, c, d) = (5, 8, 2, 4)

1.5+8+2+4=19
2.10+8+2=20
3.5+8+8=21
4.16+2+4=22

a+b+c+d=19 ---------------------0

2a+b+c=20 --------------------- 1

a+b+2d=21 ------------------------2

2b+c+d=22 ------------------------4



2a+b+c=20 ------1
a+b+2d=21-----------2

2 -1

a + c -2d = -1
>a + c = -1 + 2d

a+b+c+d=19 ------------------0
>(-1 + 2d) +b +d =19

3d+b =20---------*



a+b+2d=21 ---------2
乘2
>2a + 2b +4d =42-----------3
2b +c +d =22 ----------------4

3-4

2a - c +3d =20 -------------5
2a+b+c=20 ------1

5 -1
-2c - b +3d =0 -----------6
3d+b =20------------*
*- 6
2b +2c =20
>b+c =10
a+b+c+d=19 ------------------0
>10 + a + d =19
a+d=9 ------------------&



2a+b+c=20 ------1
2b +c +d =22 ----------------4
4-1
>b +d -2a =2 --------------7
a+b+2d=21 ---------2
2-7
3a + d =19----------------------%
a+d=9 ------------------&
%-&
2a =10
a =5
put a =5 into &
5+d =9
>d=4
put d =4 into *
3(4)+b=20
b=8

put a , b ,d into 0
5 + 4 +8 +c =19
c=2
SO.. a =5 b =8 c= 2 d = 4

5,8,2,4.....................