Mathematics
语言：中文
Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 3x -1y -1z = 0    (1)
 
9
2
x + 3y = 90    (2)
- 
21
2
x + 5z = 0    (3)
Question solving process:

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 2, the equation can be obtained:
         
9
2
x - 
3
2
y - 
3
2
z = 0    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 3x -1y -1z = 0    (1)
 
9
2
y + 
3
2
z = 90    (2)
- 
21
2
x + 5z = 0    (3)

Multiply both sides of equation (1) by 7
Divide the two sides of equation (1) by 2, the equation can be obtained:
         
21
2
x - 
7
2
y - 
7
2
z = 0    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 3x -1y -1z = 0    (1)
 
9
2
y + 
3
2
z = 90    (2)
- 
7
2
y + 
3
2
z = 0    (3)

Multiply both sides of equation (2) by 7
Divide the two sides of equation (2) by 9, the equation can be obtained:
         
7
2
y + 
7
6
z = 70    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 3x -1y -1z = 0    (1)
 
9
2
y + 
3
2
z = 90    (2)
 
8
3
z = 70    (3)

Multiply both sides of equation (3) by 9
Divide both sides of equation (3) by 16, get the equation：
         
3
2
z = 
315
8
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
 3x -1y -1z = 0    (1)
 
9
2
y = 
405
8
    (2)
 
8
3
z = 70    (3)

Multiply both sides of equation (3) by 3
Divide both sides of equation (3) by 8, get the equation：
         z = 
105
4
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 3x -1y = 
105
4
    (1)
 
9
2
y = 
405
8
    (2)
 
8
3
z = 70    (3)

Multiply both sides of equation (2) by 2
Divide both sides of equation (2) by 9, get the equation：
         y = 
45
4
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 3x = 
75
2
    (1)
 
9
2
y = 
405
8
    (2)
 z = 
105
4
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
25
2
    (1)
 y = 
45
4
    (2)
 z = 
105
4
    (3)


Therefore, the solution of the equation set is:
x = 
25
2
y = 
45
4
z = 
105
4


Convert the solution of the equation set to decimals:
x = 12.500000
y = 11.250000
z = 26.250000

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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