Mathematics
语言：中文
Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 5x + 
5
2
y + 
15
8
z = 
351
40
    (1)
 
27
10
x + 
17
10
y + 
17
10
z = 
57
10
    (2)
 
17
10
x + 
17
10
y + 
17
10
z = 
47
10
    (3)
Question solving process:

Multiply both sides of equation (1) by 27
Divide the two sides of equation (1) by 50, the equation can be obtained:
         
27
10
x + 
27
20
y + 
81
80
z = 
9477
2000
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 5x + 
5
2
y + 
15
8
z = 
351
40
    (1)
 
7
20
y + 
11
16
z = 
1923
2000
    (2)
 
17
10
x + 
17
10
y + 
17
10
z = 
47
10
    (3)

Multiply both sides of equation (1) by 17
Divide the two sides of equation (1) by 50, the equation can be obtained:
         
17
10
x + 
17
20
y + 
51
80
z = 
5967
2000
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 5x + 
5
2
y + 
15
8
z = 
351
40
    (1)
 
7
20
y + 
11
16
z = 
1923
2000
    (2)
 
17
20
y + 
17
16
z = 
3433
2000
    (3)

Multiply both sides of equation (2) by 17
Divide the two sides of equation (2) by 7, the equation can be obtained:
         
17
20
y + 
187
112
z = 
32691
14000
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 5x + 
5
2
y + 
15
8
z = 
351
40
    (1)
 
7
20
y + 
11
16
z = 
1923
2000
    (2)
- 
17
28
z = - 
433
700
    (3)

Multiply both sides of equation (3) by 77
Divide both sides of equation (3) by 68, get the equation：
        - 
11
16
z = - 
4763
6800
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 5x + 
5
2
y + 
15
8
z = 
351
40
    (1)
 
7
20
y = 
2219
8500
    (2)
- 
17
28
z = - 
433
700
    (3)

Multiply both sides of equation (3) by 105
Divide both sides of equation (3) by 34, get the equation：
        - 
15
8
z = - 
1299
680
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 5x + 
5
2
y = 
1167
170
    (1)
 
7
20
y = 
2219
8500
    (2)
- 
17
28
z = - 
433
700
    (3)

Multiply both sides of equation (2) by 50
Divide both sides of equation (2) by 7, get the equation：
         
5
2
y = 
317
170
    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation：
 5x = 5    (1)
 
7
20
y = 
2219
8500
    (2)
 z = 
433
425
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 1    (1)
 y = 
317
425
    (2)
 z = 
433
425
    (3)


Therefore, the solution of the equation set is:
x = 1
y = 
317
425
z = 
433
425


Convert the solution of the equation set to decimals:
x = 1
y = 0.745882
z = 1.018824

解方程组的详细方法请参阅：《多元一次方程组的解法》
Return