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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:
 
43
2
A - 
35
2
B - 
5
2
C = 0    (1)
- 
35
2
A + 
51
2
B + 
21
2
C + D = -14    (2)
- 
5
2
A + 
21
2
B + 
25
2
C = -14    (3)
 
3
2
A -1B = 0    (4)
Question solving process:

Multiply both sides of equation (1) by 35
Divide the two sides of equation (1) by 43, the equation can be obtained:
         
35
2
A - 
1225
86
B - 
175
86
C = 0    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 
43
2
A - 
35
2
B - 
5
2
C = 0    (1)
 
484
43
B + 
364
43
C + D = -14    (2)
- 
5
2
A + 
21
2
B + 
25
2
C = -14    (3)
 
3
2
A -1B = 0    (4)

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 43, the equation can be obtained:
         
5
2
A - 
175
86
B - 
25
86
C = 0    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 
43
2
A - 
35
2
B - 
5
2
C = 0    (1)
 
484
43
B + 
364
43
C + D = -14    (2)
 
364
43
B + 
525
43
C = -14    (3)
 
3
2
A -1B = 0    (4)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 43, the equation can be obtained:
         
3
2
A - 
105
86
B - 
15
86
C = 0    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 
43
2
A - 
35
2
B - 
5
2
C = 0    (1)
 
484
43
B + 
364
43
C + D = -14    (2)
 
364
43
B + 
525
43
C = -14    (3)
 
19
86
B + 
15
86
C = 0    (4)

Multiply both sides of equation (2) by 91
Divide the two sides of equation (2) by 121, the equation can be obtained:
         
364
43
B + 
33124
5203
C + 
91
121
D = - 
1274
121
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 
43
2
A - 
35
2
B - 
5
2
C = 0    (1)
 
484
43
B + 
364
43
C + D = -14    (2)
 
707
121
C - 
91
121
D = - 
420
121
    (3)
 
19
86
B + 
15
86
C = 0    (4)

Multiply both sides of equation (2) by 19
Divide the two sides of equation (2) by 968, the equation can be obtained:
         
19
86
B + 
1729
10406
C + 
19
968
D = - 
133
484
    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 
43
2
A - 
35
2
B - 
5
2
C = 0    (1)
 
484
43
B + 
364
43
C + D = -14    (2)
 
707
121
C - 
91
121
D = - 
420
121
    (3)
 
1
121
C - 
817
41624
D = 
133
484
    (4)

Divide the two sides of equation (3) by 707, the equation can be obtained:
         
101
12221
C - 
13
12221
D = - 
60
12221
    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 
43
2
A - 
35
2
B - 
5
2
C = 0    (1)
 
484
43
B + 
364
43
C + D = -14    (2)
 
707
121
C - 
91
121
D = - 
420
121
    (3)
- 
645
34744
D = 
113
404
    (4)

Multiply both sides of equation (4) by 3161704
Divide both sides of equation (4) by 78045, get the equation：
        - 
9191
12221
D = 
20566
1815
    (11)
, then subtract both sides of equation (11) from both sides of equation (3), get the equation：
 
43
2
A - 
35
2
B - 
5
2
C = 0    (1)
 
484
43
B + 
364
43
C + D = -14    (2)
 
707
121
C = - 
26866
1815
    (3)
- 
645
34744
D = 
113
404
    (4)

Multiply both sides of equation (4) by 34744
Divide both sides of equation (4) by 645, get the equation：
        - 
101
101
D = 
22826
1515
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 
43
2
A - 
35
2
B - 
5
2
C = 0    (1)
 
484
43
B + 
364
43
C = 
1616
1515
    (2)
 
707
121
C = - 
26866
1815
    (3)
- 
645
34744
D = 
113
404
    (4)

Multiply both sides of equation (3) by 6292
Divide both sides of equation (3) by 4343, get the equation：
         
36764
4343
C = - 
13832
645
    (13)
, then subtract both sides of equation (13) from both sides of equation (2), get the equation：
 
43
2
A - 
35
2
B - 
5
2
C = 0    (1)
 
484
43
B = 
97768
4343
    (2)
 
707
121
C = - 
26866
1815
    (3)
 D = - 
22826
1515
    (4)

Multiply both sides of equation (3) by 605
Divide both sides of equation (3) by 1414, get the equation：
         
505
202
C = - 
1919
303
    (14)
, then add the two sides of equation (14) to both sides of equation (1), get the equation：
 
43
2
A - 
35
2
B = - 
1919
303
    (1)
 
484
43
B = 
97768
4343
    (2)
 
707
121
C = - 
26866
1815
    (3)
 D = - 
22826
1515
    (4)

Multiply both sides of equation (2) by 1505
Divide both sides of equation (2) by 968, get the equation：
         
35
2
B = 
3535
101
    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 
43
2
A = 
8686
303
    (1)
 
484
43
B = 
97768
4343
    (2)
 C = - 
3838
1515
    (3)
 D = - 
22826
1515
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
404
303
    (1)
 B = 
202
101
    (2)
 C = - 
3838
1515
    (3)
 D = - 
22826
1515
    (4)


Therefore, the solution of the equation set is:
A = 
404
303
B = 
202
101
C = - 
3838
1515
D = - 
22826
1515


Convert the solution of the equation set to decimals:
A = 1.333333
B = 2.000000
C = -2.533333
D = -15.066667

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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