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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:
 4A + 9B + 4C + 5D + 6E = 53    (1)
 8A + 6B + 6C + 4D + 7E = 84    (2)
 6A + 5B + 2C + 8D + 4E = 53    (3)
 6A + 5B + 2C + 8D + 9E = 43    (4)
 6A + 8B + 2C + 5D + E = 81    (5)
Question solving process:

Multiply both sides of equation (1) by 2, the equation can be obtained:
         8A + 18B + 8C + 10D + 12E = 106    (6)
, then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D -5E = -22    (2)
 6A + 5B + 2C + 8D + 4E = 53    (3)
 6A + 5B + 2C + 8D + 9E = 43    (4)
 6A + 8B + 2C + 5D + E = 81    (5)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 2, the equation can be obtained:
         6A + 
27
2
B + 6C + 
15
2
D + 9E = 
159
2
    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D -5E = -22    (2)
- 
17
2
B -4C + 
1
2
D -5E = - 
53
2
    (3)
 6A + 5B + 2C + 8D + 9E = 43    (4)
 6A + 8B + 2C + 5D + E = 81    (5)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 2, the equation can be obtained:
         6A + 
27
2
B + 6C + 
15
2
D + 9E = 
159
2
    (8)
, then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D -5E = -22    (2)
- 
17
2
B -4C + 
1
2
D -5E = - 
53
2
    (3)
- 
17
2
B -4C + 
1
2
D = - 
73
2
    (4)
 6A + 8B + 2C + 5D + E = 81    (5)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 2, the equation can be obtained:
         6A + 
27
2
B + 6C + 
15
2
D + 9E = 
159
2
    (9)
, then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D -5E = -22    (2)
- 
17
2
B -4C + 
1
2
D -5E = - 
53
2
    (3)
- 
17
2
B -4C + 
1
2
D = - 
73
2
    (4)
- 
11
2
B -4C - 
5
2
D -8E = 
3
2
    (5)

Multiply both sides of equation (2) by 17
Divide the two sides of equation (2) by 24, the equation can be obtained:
        - 
17
2
B - 
17
12
C - 
17
4
D - 
85
24
E = - 
187
12
    (10)
, then subtract both sides of equation (10) from both sides of equation (3), the equations are reduced to:
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D -5E = -22    (2)
- 
31
12
C + 
19
4
D - 
35
24
E = - 
131
12
    (3)
- 
17
2
B -4C + 
1
2
D = - 
73
2
    (4)
- 
11
2
B -4C - 
5
2
D -8E = 
3
2
    (5)

Multiply both sides of equation (2) by 17
Divide the two sides of equation (2) by 24, the equation can be obtained:
        - 
17
2
B - 
17
12
C - 
17
4
D - 
85
24
E = - 
187
12
    (11)
, then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D -5E = -22    (2)
- 
31
12
C + 
19
4
D - 
35
24
E = - 
131
12
    (3)
- 
31
12
C + 
19
4
D + 
85
24
E = - 
251
12
    (4)
- 
11
2
B -4C - 
5
2
D -8E = 
3
2
    (5)

Multiply both sides of equation (2) by 11
Divide the two sides of equation (2) by 24, the equation can be obtained:
        - 
11
2
B - 
11
12
C - 
11
4
D - 
55
24
E = - 
121
12
    (12)
, then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D -5E = -22    (2)
- 
31
12
C + 
19
4
D - 
35
24
E = - 
131
12
    (3)
- 
31
12
C + 
19
4
D + 
85
24
E = - 
251
12
    (4)
- 
37
12
C + 
1
4
D - 
137
24
E = 
139
12
    (5)

Subtract both sides of equation (3) from both sides of equation (4) ,the equations are reduced to:
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D -5E = -22    (2)
- 
31
12
C + 
19
4
D - 
35
24
E = - 
131
12
    (3)
 5E = -10    (4)
- 
37
12
C + 
1
4
D - 
137
24
E = 
139
12
    (5)

Multiply both sides of equation (3) by 37
Divide the two sides of equation (3) by 31, the equation can be obtained:
        - 
37
12
C + 
703
124
D - 
1295
744
E = - 
4847
372
    (13)
, then subtract both sides of equation (13) from both sides of equation (5), the equations are reduced to:
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D -5E = -22    (2)
- 
31
12
C + 
19
4
D - 
35
24
E = - 
131
12
    (3)
 5E = -10    (4)
- 
168
31
D - 
123
31
E = 
763
31
    (5)

交After the exchange of equation (4) and equation (5)， the equation system becomes:
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D -5E = -22    (2)
- 
31
12
C + 
19
4
D - 
35
24
E = - 
131
12
    (3)
- 
168
31
D - 
123
31
E = 
763
31
    (4)
 5E = -10    (5)

Multiply both sides of equation (5) by 123
Divide both sides of equation (5) by 155, get the equation：
         
123
31
E = - 
246
31
    (14)
, then add the two sides of equation (14) to both sides of equation (4), get the equation：
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D -5E = -22    (2)
- 
31
12
C + 
19
4
D - 
35
24
E = - 
131
12
    (3)
- 
168
31
D = 
517
31
    (4)
 5E = -10    (5)

Multiply both sides of equation (5) by 7
Divide both sides of equation (5) by 24, get the equation：
         
35
24
E = - 
35
12
    (15)
, then add the two sides of equation (15) to both sides of equation (3), get the equation：
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D -5E = -22    (2)
- 
31
12
C + 
19
4
D = - 
83
6
    (3)
- 
168
31
D = 
517
31
    (4)
 5E = -10    (5)

Add both sides of equation (5) to both sides of equation (2), get the equation：
 4A + 9B + 4C + 5D + 6E = 53    (1)
-12B -2C -6D = -32    (2)
- 
31
12
C + 
19
4
D = - 
83
6
    (3)
- 
168
31
D = 
517
31
    (4)
 5E = -10    (5)

Multiply both sides of equation (5) by 6
Divide both sides of equation (5) by 5, get the equation：
         6E = -12    (16)
, then subtract both sides of equation (16) from both sides of equation (1), get the equation：
 4A + 9B + 4C + 5D = 65    (1)
-12B -2C -6D = -32    (2)
- 
31
12
C + 
19
4
D = - 
83
6
    (3)
- 
168
31
D = 
517
31
    (4)
 5E = -10    (5)

Multiply both sides of equation (4) by 589
Divide both sides of equation (4) by 672, get the equation：
        - 
19
4
D = 
9823
672
    (17)
, then add the two sides of equation (17) to both sides of equation (3), get the equation：
 4A + 9B + 4C + 5D = 65    (1)
-12B -2C -6D = -32    (2)
- 
31
12
C = 
527
672
    (3)
- 
168
31
D = 
517
31
    (4)
 E = -2    (5)

Multiply both sides of equation (4) by 31
Divide both sides of equation (4) by 28, get the equation：
        -6D = 
517
28
    (18)
, then subtract both sides of equation (18) from both sides of equation (2), get the equation：
 4A + 9B + 4C + 5D = 65    (1)
-12B -2C = - 
1413
28
    (2)
- 
31
12
C = 
527
672
    (3)
- 
168
31
D = 
517
31
    (4)
 E = -2    (5)

Multiply both sides of equation (4) by 155
Divide both sides of equation (4) by 168, get the equation：
        -5D = 
2585
168
    (19)
, then add the two sides of equation (19) to both sides of equation (1), get the equation：
 4A + 9B + 4C = 
13505
168
    (1)
-12B -2C = - 
1413
28
    (2)
- 
31
12
C = 
527
672
    (3)
- 
168
31
D = 
517
31
    (4)
 E = -2    (5)

Multiply both sides of equation (3) by 24
Divide both sides of equation (3) by 31, get the equation：
        -2C = 
17
28
    (20)
, then subtract both sides of equation (20) from both sides of equation (2), get the equation：
 4A + 9B + 4C = 
13505
168
    (1)
-12B = - 
715
14
    (2)
- 
31
12
C = 
527
672
    (3)
 D = - 
517
168
    (4)
 E = -2    (5)

Multiply both sides of equation (3) by 48
Divide both sides of equation (3) by 31, get the equation：
        -4C = 
17
14
    (21)
, then add the two sides of equation (21) to both sides of equation (1), get the equation：
 4A + 9B = 
13709
168
    (1)
-12B = - 
715
14
    (2)
- 
31
12
C = 
527
672
    (3)
 D = - 
517
168
    (4)
 E = -2    (5)

Multiply both sides of equation (2) by 3
Divide both sides of equation (2) by 4, get the equation：
        -9B = - 
2145
56
    (22)
, then add the two sides of equation (22) to both sides of equation (1), get the equation：
 4A = 
3637
84
    (1)
-12B = - 
715
14
    (2)
 C = - 
17
56
    (3)
 D = - 
517
168
    (4)
 E = -2    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
3637
336
    (1)
 B = 
715
168
    (2)
 C = - 
17
56
    (3)
 D = - 
517
168
    (4)
 E = -2    (5)


Therefore, the solution of the equation set is:
A = 
3637
336
B = 
715
168
C = - 
17
56
D = - 
517
168
E = -2


Convert the solution of the equation set to decimals:
A = 10.824405
B = 4.255952
C = -0.303571
D = -3.077381
E = -2

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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