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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:
 100x + 10y + z = 
27
50
    (1)
 144x + 12y + z = 
27
100
    (2)
 196x + 14y + z = 
17
100
    (3)
Question solving process:

Multiply both sides of equation (1) by 36
Divide the two sides of equation (1) by 25, the equation can be obtained:
         144x + 
72
5
y + 
36
25
z = 
486
625
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 100x + 10y + z = 
27
50
    (1)
- 
12
5
y - 
11
25
z = - 
1269
2500
    (2)
 196x + 14y + z = 
17
100
    (3)

Multiply both sides of equation (1) by 49
Divide the two sides of equation (1) by 25, the equation can be obtained:
         196x + 
98
5
y + 
49
25
z = 
1323
1250
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 100x + 10y + z = 
27
50
    (1)
- 
12
5
y - 
11
25
z = - 
1269
2500
    (2)
- 
28
5
y - 
24
25
z = - 
2221
2500
    (3)

Multiply both sides of equation (2) by 7
Divide the two sides of equation (2) by 3, the equation can be obtained:
        - 
28
5
y - 
77
75
z = - 
2961
2500
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 100x + 10y + z = 
27
50
    (1)
- 
12
5
y - 
11
25
z = - 
1269
2500
    (2)
 
1
15
z = 
37
125
    (3)

Multiply both sides of equation (3) by 33
Divide both sides of equation (3) by 5, get the equation：
         
11
25
z = 
1221
625
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation：
 100x + 10y + z = 
27
50
    (1)
- 
12
5
y = 
723
500
    (2)
 
1
15
z = 
37
125
    (3)

Multiply both sides of equation (3) by 15, get the equation：
         z = 
111
25
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 100x + 10y = - 
39
10
    (1)
- 
12
5
y = 
723
500
    (2)
 
1
15
z = 
37
125
    (3)

Multiply both sides of equation (2) by 25
Divide both sides of equation (2) by 6, get the equation：
        -10y = 
241
40
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 100x = 
17
8
    (1)
- 
12
5
y = 
723
500
    (2)
 z = 
111
25
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
17
800
    (1)
 y = - 
241
400
    (2)
 z = 
111
25
    (3)


Therefore, the solution of the equation set is:
x = 
17
800
y = - 
241
400
z = 
111
25


Convert the solution of the equation set to decimals:
x = 0.021250
y = -0.602500
z = 4.440000

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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