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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:
 12x + 7y -6z = 30    (1)
 7x + 12y -2z = 10    (2)
 3x + y -5z = 5    (3)
Question solving process:

Multiply both sides of equation (1) by 7
Divide the two sides of equation (1) by 12, the equation can be obtained:
         7x + 
49
12
y - 
7
2
z = 
35
2
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 12x + 7y -6z = 30    (1)
 
95
12
y + 
3
2
z = - 
15
2
    (2)
 3x + y -5z = 5    (3)

Divide the two sides of equation (1) by 4, the equation can be obtained:
         3x + 
7
4
y - 
3
2
z = 
15
2
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 12x + 7y -6z = 30    (1)
 
95
12
y + 
3
2
z = - 
15
2
    (2)
- 
3
4
y - 
7
2
z = - 
5
2
    (3)

Multiply both sides of equation (2) by 9
Divide the two sides of equation (2) by 95, the equation can be obtained:
         
3
4
y + 
27
190
z = - 
27
38
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 12x + 7y -6z = 30    (1)
 
95
12
y + 
3
2
z = - 
15
2
    (2)
- 
319
95
z = - 
61
19
    (3)

Multiply both sides of equation (3) by 285
Divide both sides of equation (3) by 638, get the equation：
        - 
3
2
z = - 
915
638
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 12x + 7y -6z = 30    (1)
 
95
12
y = - 
2850
319
    (2)
- 
319
95
z = - 
61
19
    (3)

Multiply both sides of equation (3) by 570
Divide both sides of equation (3) by 319, get the equation：
        -6z = - 
1830
319
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 12x + 7y = 
11400
319
    (1)
 
95
12
y = - 
2850
319
    (2)
- 
319
95
z = - 
61
19
    (3)

Multiply both sides of equation (2) by 84
Divide both sides of equation (2) by 95, get the equation：
         7y = - 
2520
319
    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation：
 12x = 
13920
319
    (1)
 
95
12
y = - 
2850
319
    (2)
 z = 
305
319
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
1160
319
    (1)
 y = - 
360
319
    (2)
 z = 
305
319
    (3)


Therefore, the solution of the equation set is:
x = 
1160
319
y = - 
360
319
z = 
305
319


Convert the solution of the equation set to decimals:
x = 3.636364
y = -1.128527
z = 0.956113

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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