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Multivariate equation
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On line solution of multivariate equations：
    First set the elements of the equation (i.e. the number of unknowns), then click the "Next" button to enter the coefficients of each element of the equation set, and click the "Next" button to obtain the solution of the equation set.
    Note that the coefficients of each element of the equation system can only be numbers, not algebraic expressions (including mathematical functions).
    Current location：Equations > Multivariate equations > Answer
detailed information：
The input equation set is:
 x + 
27
5
y + 
144
5
z = 
3
10
    (1)
 x + 
28
5
y + 
159
5
z = - 
9
5
    (2)
 x + 
19
5
y + 
74
5
z = - 
9
5
    (3)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 x + 
27
5
y + 
144
5
z = 
3
10
    (1)
 
1
5
y + 3z = - 
21
10
    (2)
 x + 
19
5
y + 
74
5
z = - 
9
5
    (3)

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 x + 
27
5
y + 
144
5
z = 
3
10
    (1)
 
1
5
y + 3z = - 
21
10
    (2)
- 
8
5
y -14z = - 
21
10
    (3)

Multiply both sides of equation (2) by 8, the equation can be obtained:
         
8
5
y + 24z = - 
84
5
    (4)
, then add the two sides of equation (4) to both sides of equation (3), the equations are reduced to:
 x + 
27
5
y + 
144
5
z = 
3
10
    (1)
 
1
5
y + 3z = - 
21
10
    (2)
 10z = - 
189
10
    (3)

Multiply both sides of equation (3) by 3
Divide both sides of equation (3) by 10, get the equation：
         3z = - 
567
100
    (5)
, then subtract both sides of equation (5) from both sides of equation (2), get the equation：
 x + 
27
5
y + 
144
5
z = 
3
10
    (1)
 
1
5
y = 
357
100
    (2)
 10z = - 
189
10
    (3)

Multiply both sides of equation (3) by 72
Divide both sides of equation (3) by 25, get the equation：
         
144
5
z = - 
6804
125
    (6)
, then subtract both sides of equation (6) from both sides of equation (1), get the equation：
 x + 
27
5
y = 
13683
250
    (1)
 
1
5
y = 
357
100
    (2)
 10z = - 
189
10
    (3)

Multiply both sides of equation (2) by 27, get the equation：
         
27
5
y = 
9639
100
    (7)
, then subtract both sides of equation (7) from both sides of equation (1), get the equation：
 x = - 
20829
500
    (1)
 
1
5
y = 
357
100
    (2)
 z = - 
189
100
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = - 
20829
500
    (1)
 y = 
357
20
    (2)
 z = - 
189
100
    (3)


Therefore, the solution of the equation set is:
x = - 
20829
500
y = 
357
20
z = - 
189
100


Convert the solution of the equation set to decimals:
x = -41.658000
y = 17.850000
z = -1.890000

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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