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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:
 15x + 11y + 19z = -3    (1)
 11x + 36y + 3z = 6    (2)
 19x + 3y + 31z = -5    (3)
Question solving process:

Multiply both sides of equation (1) by 11
Divide the two sides of equation (1) by 15, the equation can be obtained:
         11x + 
121
15
y + 
209
15
z = - 
11
5
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 15x + 11y + 19z = -3    (1)
 
419
15
y - 
164
15
z = 
41
5
    (2)
 19x + 3y + 31z = -5    (3)

Multiply both sides of equation (1) by 19
Divide the two sides of equation (1) by 15, the equation can be obtained:
         19x + 
209
15
y + 
361
15
z = - 
19
5
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 15x + 11y + 19z = -3    (1)
 
419
15
y - 
164
15
z = 
41
5
    (2)
- 
164
15
y + 
104
15
z = - 
6
5
    (3)

Multiply both sides of equation (2) by 164
Divide the two sides of equation (2) by 419, the equation can be obtained:
         
68716
6285
y - 
26896
6285
z = 
6724
2095
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 15x + 11y + 19z = -3    (1)
 
419
15
y - 
164
15
z = 
41
5
    (2)
 
1112
419
z = 
842
419
    (3)

Multiply both sides of equation (3) by 17179
Divide both sides of equation (3) by 4170, get the equation：
         
68716
6285
z = 
17261
2085
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 15x + 11y + 19z = -3    (1)
 
419
15
y = 
34358
2085
    (2)
 
1112
419
z = 
842
419
    (3)

Multiply both sides of equation (3) by 7961
Divide both sides of equation (3) by 1112, get the equation：
         
7961
419
z = 
7999
556
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 15x + 11y = - 
9667
556
    (1)
 
419
15
y = 
34358
2085
    (2)
 
1112
419
z = 
842
419
    (3)

Multiply both sides of equation (2) by 165
Divide both sides of equation (2) by 419, get the equation：
         
4609
419
y = 
377938
58241
    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation：
 15x = - 
13275
556
    (1)
 
419
15
y = 
34358
2085
    (2)
 z = 
421
556
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = - 
885
556
    (1)
 y = 
34358
58241
    (2)
 z = 
421
556
    (3)


Therefore, the solution of the equation set is:
x = - 
885
556
y = 
34358
58241
z = 
421
556


Convert the solution of the equation set to decimals:
x = -1.591727
y = 0.589928
z = 0.757194

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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