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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:
 30x + 10y + 6z = 15    (1)
 70x + 42y + 30z = 
105
2
    (2)
 126x + 90y + 70z = 105    (3)
Question solving process:

Multiply both sides of equation (1) by 7
Divide the two sides of equation (1) by 3, the equation can be obtained:
         70x + 
70
3
y + 14z = 35    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 30x + 10y + 6z = 15    (1)
 
56
3
y + 16z = 
35
2
    (2)
 126x + 90y + 70z = 105    (3)

Multiply both sides of equation (1) by 21
Divide the two sides of equation (1) by 5, the equation can be obtained:
         126x + 42y + 
126
5
z = 63    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 30x + 10y + 6z = 15    (1)
 
56
3
y + 16z = 
35
2
    (2)
 48y + 
224
5
z = 42    (3)

Multiply both sides of equation (2) by 18
Divide the two sides of equation (2) by 7, the equation can be obtained:
         48y + 
288
7
z = 45    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 30x + 10y + 6z = 15    (1)
 
56
3
y + 16z = 
35
2
    (2)
 
128
35
z = -3    (3)

Multiply both sides of equation (3) by 35
Divide both sides of equation (3) by 8, get the equation：
         16z = - 
105
8
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
 30x + 10y + 6z = 15    (1)
 
56
3
y = 
245
8
    (2)
 
128
35
z = -3    (3)

Multiply both sides of equation (3) by 105
Divide both sides of equation (3) by 64, get the equation：
         6z = - 
315
64
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 30x + 10y = 
1275
64
    (1)
 
56
3
y = 
245
8
    (2)
 
128
35
z = -3    (3)

Multiply both sides of equation (2) by 15
Divide both sides of equation (2) by 28, get the equation：
         10y = 
525
32
    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation：
 30x = 
225
64
    (1)
 
56
3
y = 
245
8
    (2)
 z = - 
105
128
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
15
128
    (1)
 y = 
105
64
    (2)
 z = - 
105
128
    (3)


Therefore, the solution of the equation set is:
x = 
15
128
y = 
105
64
z = - 
105
128


Convert the solution of the equation set to decimals:
x = 0.117188
y = 1.640625
z = -0.820312

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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