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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:
 20x -10y -8z = 33    (1)
-10x + 24y -8z = 
61
5
    (2)
-8x -4y + 20z = - 
61
5
    (3)
Question solving process:

Divide the two sides of equation (1) by 2, the equation can be obtained:
         10x -5y -4z = 
33
2
    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
 20x -10y -8z = 33    (1)
 19y -12z = 
287
10
    (2)
-8x -4y + 20z = - 
61
5
    (3)

Multiply both sides of equation (1) by 2
Divide the two sides of equation (1) by 5, the equation can be obtained:
         8x -4y - 
16
5
z = 
66
5
    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 20x -10y -8z = 33    (1)
 19y -12z = 
287
10
    (2)
-8y + 
84
5
z = 1    (3)

Multiply both sides of equation (2) by 8
Divide the two sides of equation (2) by 19, the equation can be obtained:
         8y - 
96
19
z = 
1148
95
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 20x -10y -8z = 33    (1)
 19y -12z = 
287
10
    (2)
 
1116
95
z = 
1243
95
    (3)

Multiply both sides of equation (3) by 95
Divide both sides of equation (3) by 93, get the equation：
         12z = 
1243
93
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 20x -10y -8z = 33    (1)
 19y = 
39121
930
    (2)
 
1116
95
z = 
1243
95
    (3)

Multiply both sides of equation (3) by 190
Divide both sides of equation (3) by 279, get the equation：
         8z = 
2486
279
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 20x -10y = 
11693
279
    (1)
 19y = 
39121
930
    (2)
 
1116
95
z = 
1243
95
    (3)

Multiply both sides of equation (2) by 10
Divide both sides of equation (2) by 19, get the equation：
         10y = 
2059
93
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 20x = 
17870
279
    (1)
 19y = 
39121
930
    (2)
 z = 
1243
1116
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
1787
558
    (1)
 y = 
2059
930
    (2)
 z = 
1243
1116
    (3)


Therefore, the solution of the equation set is:
x = 
1787
558
y = 
2059
930
z = 
1243
1116


Convert the solution of the equation set to decimals:
x = 3.202509
y = 2.213978
z = 1.113799

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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