Mathematics
语言：中文
Language:English
current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 
6
5
x + 
3
2
y + 
11
5
z = 200    (1)
 x + y -1z = 0    (2)
 x + y + z = 100    (3)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 6, the equation can be obtained:
         x + 
5
4
y + 
11
6
z = 
500
3
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 
6
5
x + 
3
2
y + 
11
5
z = 200    (1)
- 
1
4
y - 
17
6
z = - 
500
3
    (2)
 x + y + z = 100    (3)

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 6, the equation can be obtained:
         x + 
5
4
y + 
11
6
z = 
500
3
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 
6
5
x + 
3
2
y + 
11
5
z = 200    (1)
- 
1
4
y - 
17
6
z = - 
500
3
    (2)
- 
1
4
y - 
5
6
z = - 
200
3
    (3)

Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
 
6
5
x + 
3
2
y + 
11
5
z = 200    (1)
- 
1
4
y - 
17
6
z = - 
500
3
    (2)
 2z = 100    (3)

Multiply both sides of equation (3) by 17
Divide both sides of equation (3) by 12, get the equation：
         
17
6
z = 
425
3
    (6)
, then add the two sides of equation (6) to both sides of equation (2), get the equation：
 
6
5
x + 
3
2
y + 
11
5
z = 200    (1)
- 
1
4
y = -25    (2)
 2z = 100    (3)

Multiply both sides of equation (3) by 11
Divide both sides of equation (3) by 10, get the equation：
         
11
5
z = 110    (7)
, then subtract both sides of equation (7) from both sides of equation (1), get the equation：
 
6
5
x + 
3
2
y = 90    (1)
- 
1
4
y = -25    (2)
 2z = 100    (3)

Multiply both sides of equation (2) by 6, get the equation：
        - 
3
2
y = -150    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 
6
5
x = -60    (1)
- 
1
4
y = -25    (2)
 z = 50    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = -50    (1)
 y = 100    (2)
 z = 50    (3)


Therefore, the solution of the equation set is:
x = -50
y = 100
z = 50

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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