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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:
 19x -1y -6z = 24    (1)
-1x + 17y -4z = 0    (2)
-6x -4y + 10z = -12    (3)
Question solving process:

Divide the two sides of equation (1) by 19, the equation can be obtained:
         x - 
1
19
y - 
6
19
z = 
24
19
    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
 19x -1y -6z = 24    (1)
 
322
19
y - 
82
19
z = 
24
19
    (2)
-6x -4y + 10z = -12    (3)

Multiply both sides of equation (1) by 6
Divide the two sides of equation (1) by 19, the equation can be obtained:
         6x - 
6
19
y - 
36
19
z = 
144
19
    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 19x -1y -6z = 24    (1)
 
322
19
y - 
82
19
z = 
24
19
    (2)
- 
82
19
y + 
154
19
z = - 
84
19
    (3)

Multiply both sides of equation (2) by 41
Divide the two sides of equation (2) by 161, the equation can be obtained:
         
82
19
y - 
3362
3059
z = 
984
3059
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 19x -1y -6z = 24    (1)
 
322
19
y - 
82
19
z = 
24
19
    (2)
 
1128
161
z = - 
660
161
    (3)

Multiply both sides of equation (3) by 6601
Divide both sides of equation (3) by 10716, get the equation：
         
82
19
z = - 
2255
893
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 19x -1y -6z = 24    (1)
 
322
19
y = - 
1127
893
    (2)
 
1128
161
z = - 
660
161
    (3)

Multiply both sides of equation (3) by 161
Divide both sides of equation (3) by 188, get the equation：
         6z = - 
165
47
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 19x -1y = 
963
47
    (1)
 
322
19
y = - 
1127
893
    (2)
 
1128
161
z = - 
660
161
    (3)

Multiply both sides of equation (2) by 19
Divide both sides of equation (2) by 322, get the equation：
         y = - 
7
94
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 19x = 
1919
94
    (1)
 
322
19
y = - 
1127
893
    (2)
 z = - 
55
94
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
101
94
    (1)
 y = - 
7
94
    (2)
 z = - 
55
94
    (3)


Therefore, the solution of the equation set is:
x = 
101
94
y = - 
7
94
z = - 
55
94


Convert the solution of the equation set to decimals:
x = 1.074468
y = -0.074468
z = -0.585106

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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