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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:
 10A + 
79
10
B + 
21
10
C = 
1799
10
    (1)
 
21
10
B + 
79
10
C + 10D = 
1769
10
    (2)
- 
29
10
A + 
59
10
C + 
79
10
D = 
1019
10
    (3)
 
79
10
A + 
59
10
B - 
29
10
D = 
1059
10
    (4)
Question solving process:

Multiply both sides of equation (1) by 29
Divide the two sides of equation (1) by 100, the equation can be obtained:
         
29
10
A + 
2291
1000
B + 
609
1000
C = 
52171
1000
    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 10A + 
79
10
B + 
21
10
C = 
1799
10
    (1)
 
21
10
B + 
79
10
C + 10D = 
1769
10
    (2)
 
2291
1000
B + 
6509
1000
C + 
79
10
D = 
154071
1000
    (3)
 
79
10
A + 
59
10
B - 
29
10
D = 
1059
10
    (4)

Multiply both sides of equation (1) by 79
Divide the two sides of equation (1) by 100, the equation can be obtained:
         
79
10
A + 
6241
1000
B + 
1659
1000
C = 
142121
1000
    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 10A + 
79
10
B + 
21
10
C = 
1799
10
    (1)
 
21
10
B + 
79
10
C + 10D = 
1769
10
    (2)
 
2291
1000
B + 
6509
1000
C + 
79
10
D = 
154071
1000
    (3)
- 
341
1000
B - 
1659
1000
C - 
29
10
D = - 
36221
1000
    (4)

Multiply both sides of equation (2) by 2291
Divide the two sides of equation (2) by 2100, the equation can be obtained:
         
2291
1000
B + 
180989
21000
C + 
2291
210
D = 
4052779
21000
    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 10A + 
79
10
B + 
21
10
C = 
1799
10
    (1)
 
21
10
B + 
79
10
C + 10D = 
1769
10
    (2)
- 
443
210
C - 
316
105
D = - 
102161
2625
    (3)
- 
341
1000
B - 
1659
1000
C - 
29
10
D = - 
36221
1000
    (4)

Multiply both sides of equation (2) by 341
Divide the two sides of equation (2) by 2100, the equation can be obtained:
         
341
1000
B + 
26939
21000
C + 
341
210
D = 
603229
21000
    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 10A + 
79
10
B + 
21
10
C = 
1799
10
    (1)
 
21
10
B + 
79
10
C + 10D = 
1769
10
    (2)
- 
443
210
C - 
316
105
D = - 
102161
2625
    (3)
- 
79
210
C - 
134
105
D = - 
39353
5250
    (4)

Multiply both sides of equation (3) by 79
Divide the two sides of equation (3) by 443, the equation can be obtained:
        - 
34997
93030
C - 
24964
46515
D = - 
8070719
1162875
    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 10A + 
79
10
B + 
21
10
C = 
1799
10
    (1)
 
21
10
B + 
79
10
C + 10D = 
1769
10
    (2)
- 
443
210
C - 
316
105
D = - 
102161
2625
    (3)
- 
1638
2215
D = - 
61521
110750
    (4)

Multiply both sides of equation (4) by 69994
Divide both sides of equation (4) by 17199, get the equation：
        - 
139988
46515
D = - 
1620053
716625
    (10)
, then subtract both sides of equation (10) from both sides of equation (3), get the equation：
 10A + 
79
10
B + 
21
10
C = 
1799
10
    (1)
 
21
10
B + 
79
10
C + 10D = 
1769
10
    (2)
- 
443
210
C = - 
1050796
28665
    (3)
- 
1638
2215
D = - 
61521
110750
    (4)

Multiply both sides of equation (4) by 11075
Divide both sides of equation (4) by 819, get the equation：
        - 
4430
443
D = - 
20507
2730
    (11)
, then add the two sides of equation (11) to both sides of equation (2), get the equation：
 10A + 
79
10
B + 
21
10
C = 
1799
10
    (1)
 
21
10
B + 
79
10
C = 
46243
273
    (2)
- 
443
210
C = - 
1050796
28665
    (3)
- 
1638
2215
D = - 
61521
110750
    (4)

Multiply both sides of equation (3) by 1659
Divide both sides of equation (3) by 443, get the equation：
        - 
34997
4430
C = - 
187388
1365
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 10A + 
79
10
B + 
21
10
C = 
1799
10
    (1)
 
21
10
B = 
2087
65
    (2)
- 
443
210
C = - 
1050796
28665
    (3)
 D = 
20507
27300
    (4)

Multiply both sides of equation (3) by 441
Divide both sides of equation (3) by 443, get the equation：
        - 
9303
4430
C = - 
1050796
28795
    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 10A + 
79
10
B = 
8258849
57590
    (1)
 
21
10
B = 
2087
65
    (2)
- 
443
210
C = - 
1050796
28665
    (3)
 D = 
20507
27300
    (4)

Multiply both sides of equation (2) by 79
Divide both sides of equation (2) by 21, get the equation：
         
79
10
B = 
164873
1365
    (14)
, then subtract both sides of equation (14) from both sides of equation (1), get the equation：
 10A = 
61757
2730
    (1)
 
21
10
B = 
2087
65
    (2)
 C = 
2101592
120939
    (3)
 D = 
20507
27300
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
61757
27300
    (1)
 B = 
4174
273
    (2)
 C = 
2101592
120939
    (3)
 D = 
20507
27300
    (4)


Therefore, the solution of the equation set is:
A = 
61757
27300
B = 
4174
273
C = 
2101592
120939
D = 
20507
27300


Convert the solution of the equation set to decimals:
A = 2.262161
B = 15.289377
C = 17.377289
D = 0.751172

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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