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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:
 10x + 5y + 20z = 
1146789
50
    (1)
 17x + 5y + 6z = 
557103
20
    (2)
 13x + 5y + 8z = 
506329
20
    (3)
Question solving process:

Multiply both sides of equation (1) by 17
Divide the two sides of equation (1) by 10, the equation can be obtained:
         17x + 
17
2
y + 34z = 
19495413
500
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 10x + 5y + 20z = 
1146789
50
    (1)
- 
7
2
y -28z = - 
2783919
250
    (2)
 13x + 5y + 8z = 
506329
20
    (3)

Multiply both sides of equation (1) by 13
Divide the two sides of equation (1) by 10, the equation can be obtained:
         13x + 
13
2
y + 26z = 
14908257
500
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 10x + 5y + 20z = 
1146789
50
    (1)
- 
7
2
y -28z = - 
2783919
250
    (2)
- 
3
2
y -18z = - 
562508
125
    (3)

Multiply both sides of equation (2) by 3
Divide the two sides of equation (2) by 7, the equation can be obtained:
        - 
3
2
y -12z = - 
8351757
1750
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 10x + 5y + 20z = 
1146789
50
    (1)
- 
7
2
y -28z = - 
2783919
250
    (2)
-6z = 
95329
350
    (3)

Multiply both sides of equation (3) by 14
Divide both sides of equation (3) by 3, get the equation：
        -28z = 
95329
75
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
 10x + 5y + 20z = 
1146789
50
    (1)
- 
7
2
y = - 
9305047
750
    (2)
-6z = 
95329
350
    (3)

Multiply both sides of equation (3) by 10
Divide both sides of equation (3) by 3, get the equation：
        -20z = 
95329
105
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 10x + 5y = 
25035859
1050
    (1)
- 
7
2
y = - 
9305047
750
    (2)
-6z = 
95329
350
    (3)

Multiply both sides of equation (2) by 10
Divide both sides of equation (2) by 7, get the equation：
        -5y = - 
9305047
525
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 10x = 
1285153
210
    (1)
- 
7
2
y = - 
9305047
750
    (2)
 z = - 
95329
2100
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
1285153
2100
    (1)
 y = 
9305047
2625
    (2)
 z = - 
95329
2100
    (3)


Therefore, the solution of the equation set is:
x = 
1285153
2100
y = 
9305047
2625
z = - 
95329
2100


Convert the solution of the equation set to decimals:
x = 611.977619
y = 3544.779810
z = -45.394762

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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