Mathematics
语言：中文
Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 6x -5z = -17    (1)
 7y -4z = -11    (2)
-5x -4y + 9z = 0    (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:
         5x - 
25
6
z = - 
85
6
    (4)
, then add the two sides of equation (4) to both sides of equation (3), the equations are reduced to:
 6x -5z = -17    (1)
 7y -4z = -11    (2)
-4y + 
29
6
z = - 
85
6
    (3)

Multiply both sides of equation (2) by 4
Divide the two sides of equation (2) by 7, the equation can be obtained:
         4y - 
16
7
z = - 
44
7
    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 6x -5z = -17    (1)
 7y -4z = -11    (2)
 
107
42
z = - 
859
42
    (3)

Multiply both sides of equation (3) by 168
Divide both sides of equation (3) by 107, get the equation：
         
428
107
z = - 
3436
107
    (6)
, then add the two sides of equation (6) to both sides of equation (2), get the equation：
 6x -5z = -17    (1)
 7y = - 
4613
107
    (2)
 
107
42
z = - 
859
42
    (3)

Multiply both sides of equation (3) by 210
Divide both sides of equation (3) by 107, get the equation：
         
535
107
z = - 
4295
107
    (7)
, then add the two sides of equation (7) to both sides of equation (1), get the equation：
 6x = - 
6114
107
    (1)
 7y = - 
4613
107
    (2)
 
107
42
z = - 
859
42
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = - 
1019
107
    (1)
 y = - 
659
107
    (2)
 z = - 
859
107
    (3)


Therefore, the solution of the equation set is:
x = - 
1019
107
y = - 
659
107
z = - 
859
107


Convert the solution of the equation set to decimals:
x = -9.523364
y = -6.158879
z = -8.028037

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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