Mathematics
语言：中文
Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 x + y -2z = 0    (1)
 
6
5
x - 
13
10
y - 
13
10
z = 0    (2)
 z = 
14520053
10000
    (3)
Question solving process:

Multiply both sides of equation (1) by 6
Divide the two sides of equation (1) by 5, the equation can be obtained:
         
6
5
x + 
6
5
y - 
12
5
z = 0    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 x + y -2z = 0    (1)
- 
5
2
y + 
11
10
z = 0    (2)
 z = 
14520053
10000
    (3)

Multiply both sides of equation (3) by 11
Divide both sides of equation (3) by 10, get the equation：
         
11
10
z = 
159720583
100000
    (5)
, then subtract both sides of equation (5) from both sides of equation (2), get the equation：
 x + y -2z = 0    (1)
- 
5
2
y = - 
159720583
100000
    (2)
 z = 
14520053
10000
    (3)

Multiply both sides of equation (3) by 2, get the equation：
         2z = 
14520053
5000
    (6)
, then add the two sides of equation (6) to both sides of equation (1), get the equation：
 x + y = 
14520053
5000
    (1)
- 
5
2
y = - 
159720583
100000
    (2)
 z = 
14520053
10000
    (3)

Multiply both sides of equation (2) by 2
Divide both sides of equation (2) by 5, get the equation：
        -1y = - 
159720583
250000
    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation：
 x = 
566282067
250000
    (1)
- 
5
2
y = - 
159720583
100000
    (2)
 z = 
14520053
10000
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
566282067
250000
    (1)
 y = 
159720583
250000
    (2)
 z = 
14520053
10000
    (3)


Therefore, the solution of the equation set is:
x = 
566282067
250000
y = 
159720583
250000
z = 
14520053
10000


Convert the solution of the equation set to decimals:
x = 2265.128268
y = 638.882332
z = 1452.005300

解方程组的详细方法请参阅：《多元一次方程组的解法》
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