Mathematics
语言：中文
Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 1020x + 510z = 0    (1)
 1330y + 510z = 5    (2)
-1x -1y + z = 0    (3)
Question solving process:

Divide the two sides of equation (1) by 1020, the equation can be obtained:
         x + 
1
2
z = 0    (4)
, then add the two sides of equation (4) to both sides of equation (3), the equations are reduced to:
 1020x + 510z = 0    (1)
 1330y + 510z = 5    (2)
-1y + 
3
2
z = 0    (3)

Divide the two sides of equation (2) by 1330, the equation can be obtained:
         y + 
51
133
z = 
1
266
    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 1020x + 510z = 0    (1)
 1330y + 510z = 5    (2)
 
501
266
z = 
1
266
    (3)

Multiply both sides of equation (3) by 45220
Divide both sides of equation (3) by 167, get the equation：
         
85170
167
z = 
170
167
    (6)
, then subtract both sides of equation (6) from both sides of equation (2), get the equation：
 1020x + 510z = 0    (1)
 1330y = 
665
167
    (2)
 
501
266
z = 
1
266
    (3)

Multiply both sides of equation (3) by 45220
Divide both sides of equation (3) by 167, get the equation：
         
85170
167
z = 
170
167
    (7)
, then subtract both sides of equation (7) from both sides of equation (1), get the equation：
 1020x = - 
170
167
    (1)
 1330y = 
665
167
    (2)
 
501
266
z = 
1
266
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = - 
1
1002
    (1)
 y = 
1
334
    (2)
 z = 
1
501
    (3)


Therefore, the solution of the equation set is:
x = - 
1
1002
y = 
1
334
z = 
1
501


Convert the solution of the equation set to decimals:
x = -0.000998
y = 0.002994
z = 0.001996

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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