Mathematics
语言：中文
Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 x -1y + z = 0    (1)
 25x + 5y + z = 0    (2)
 4x -2y + z = 6    (3)
Question solving process:

Multiply both sides of equation (1) by 25, the equation can be obtained:
         25x -25y + 25z = 0    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 x -1y + z = 0    (1)
 30y -24z = 0    (2)
 4x -2y + z = 6    (3)

Multiply both sides of equation (1) by 4, the equation can be obtained:
         4x -4y + 4z = 0    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 x -1y + z = 0    (1)
 30y -24z = 0    (2)
 2y -3z = 6    (3)

Divide the two sides of equation (2) by 15, the equation can be obtained:
         2y - 
8
5
z = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 x -1y + z = 0    (1)
 30y -24z = 0    (2)
- 
7
5
z = 6    (3)

Multiply both sides of equation (3) by 120
Divide both sides of equation (3) by 7, get the equation：
        -24z = 
720
7
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
 x -1y + z = 0    (1)
 30y = - 
720
7
    (2)
- 
7
5
z = 6    (3)

Multiply both sides of equation (3) by 5
Divide both sides of equation (3) by 7, get the equation：
        -1z = 
30
7
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 x -1y = 
30
7
    (1)
 30y = - 
720
7
    (2)
- 
7
5
z = 6    (3)

Divide both sides of equation (2) by 30, get the equation：
         y = - 
24
7
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 x = 
6
7
    (1)
 30y = - 
720
7
    (2)
 z = - 
30
7
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
6
7
    (1)
 y = - 
24
7
    (2)
 z = - 
30
7
    (3)


Therefore, the solution of the equation set is:
x = 
6
7
y = - 
24
7
z = - 
30
7


Convert the solution of the equation set to decimals:
x = 0.857143
y = -3.428571
z = -4.285714

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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