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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 + 3B + 3C + 5D + 3E = 21    (1)
 4A + 3B + 5C + 3D + 4E = 2    (2)
 A + 3B + 4C + 2D + 3E = 83    (3)
 5A + 2B + 4C + 5D + 2E = 99    (4)
 4A + 3B + 2C + 5D + 2E = 63    (5)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (2) ,the equations are reduced to:
 4A + 3B + 3C + 5D + 3E = 21    (1)
 2C -2D + E = -19    (2)
 A + 3B + 4C + 2D + 3E = 83    (3)
 5A + 2B + 4C + 5D + 2E = 99    (4)
 4A + 3B + 2C + 5D + 2E = 63    (5)

Divide the two sides of equation (1) by 4, the equation can be obtained:
         A + 
3
4
B + 
3
4
C + 
5
4
D + 
3
4
E = 
21
4
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 4A + 3B + 3C + 5D + 3E = 21    (1)
 2C -2D + E = -19    (2)
 
9
4
B + 
13
4
C + 
3
4
D + 
9
4
E = 
311
4
    (3)
 5A + 2B + 4C + 5D + 2E = 99    (4)
 4A + 3B + 2C + 5D + 2E = 63    (5)

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 4, the equation can be obtained:
         5A + 
15
4
B + 
15
4
C + 
25
4
D + 
15
4
E = 
105
4
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 4A + 3B + 3C + 5D + 3E = 21    (1)
 2C -2D + E = -19    (2)
 
9
4
B + 
13
4
C + 
3
4
D + 
9
4
E = 
311
4
    (3)
- 
7
4
B + 
1
4
C - 
5
4
D - 
7
4
E = 
291
4
    (4)
 4A + 3B + 2C + 5D + 2E = 63    (5)

Subtract both sides of equation (1) from both sides of equation (5) ,the equations are reduced to:
 4A + 3B + 3C + 5D + 3E = 21    (1)
 2C -2D + E = -19    (2)
 
9
4
B + 
13
4
C + 
3
4
D + 
9
4
E = 
311
4
    (3)
- 
7
4
B + 
1
4
C - 
5
4
D - 
7
4
E = 
291
4
    (4)
-1C -1E = 42    (5)

交After the exchange of equation (2) and equation (3)， the equation system becomes:
 4A + 3B + 3C + 5D + 3E = 21    (1)
 
9
4
B + 
13
4
C + 
3
4
D + 
9
4
E = 
311
4
    (2)
 2C -2D + E = -19    (3)
- 
7
4
B + 
1
4
C - 
5
4
D - 
7
4
E = 
291
4
    (4)
-1C -1E = 42    (5)

Multiply both sides of equation (2) by 7
Divide the two sides of equation (2) by 9, the equation can be obtained:
         
7
4
B + 
91
36
C + 
7
12
D + 
7
4
E = 
2177
36
    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 4A + 3B + 3C + 5D + 3E = 21    (1)
 
9
4
B + 
13
4
C + 
3
4
D + 
9
4
E = 
311
4
    (2)
 2C -2D + E = -19    (3)
 
25
9
C - 
2
3
D = 
1199
9
    (4)
-1C -1E = 42    (5)

Multiply both sides of equation (3) by 25
Divide the two sides of equation (3) by 18, the equation can be obtained:
         
25
9
C - 
25
9
D + 
25
18
E = - 
475
18
    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 4A + 3B + 3C + 5D + 3E = 21    (1)
 
9
4
B + 
13
4
C + 
3
4
D + 
9
4
E = 
311
4
    (2)
 2C -2D + E = -19    (3)
 
19
9
D - 
25
18
E = 
2873
18
    (4)
-1C -1E = 42    (5)

Divide the two sides of equation (3) by 2, the equation can be obtained:
         C -1D + 
1
2
E = - 
19
2
    (10)
, then add the two sides of equation (10) to both sides of equation (5), the equations are reduced to:
 4A + 3B + 3C + 5D + 3E = 21    (1)
 
9
4
B + 
13
4
C + 
3
4
D + 
9
4
E = 
311
4
    (2)
 2C -2D + E = -19    (3)
 
19
9
D - 
25
18
E = 
2873
18
    (4)
-1D - 
1
2
E = 
65
2
    (5)

Multiply both sides of equation (4) by 9
Divide the two sides of equation (4) by 19, the equation can be obtained:
         D - 
25
38
E = 
2873
38
    (11)
, then add the two sides of equation (11) to both sides of equation (5), the equations are reduced to:
 4A + 3B + 3C + 5D + 3E = 21    (1)
 
9
4
B + 
13
4
C + 
3
4
D + 
9
4
E = 
311
4
    (2)
 2C -2D + E = -19    (3)
 
19
9
D - 
25
18
E = 
2873
18
    (4)
- 
22
19
E = 
2054
19
    (5)

Multiply both sides of equation (5) by 475
Divide both sides of equation (5) by 396, get the equation：
        - 
25
18
E = 
25675
198
    (12)
, then subtract both sides of equation (12) from both sides of equation (4), get the equation：
 4A + 3B + 3C + 5D + 3E = 21    (1)
 
9
4
B + 
13
4
C + 
3
4
D + 
9
4
E = 
311
4
    (2)
 2C -2D + E = -19    (3)
 
19
9
D = 
988
33
    (4)
- 
22
19
E = 
2054
19
    (5)

Multiply both sides of equation (5) by 19
Divide both sides of equation (5) by 22, get the equation：
        -1E = 
1027
11
    (13)
, then add the two sides of equation (13) to both sides of equation (3), get the equation：
 4A + 3B + 3C + 5D + 3E = 21    (1)
 
9
4
B + 
13
4
C + 
3
4
D + 
9
4
E = 
311
4
    (2)
 2C -2D = 
818
11
    (3)
 
19
9
D = 
988
33
    (4)
- 
22
19
E = 
2054
19
    (5)

Multiply both sides of equation (5) by 171
Divide both sides of equation (5) by 88, get the equation：
        - 
9
4
E = 
9243
44
    (14)
, then add the two sides of equation (14) to both sides of equation (2), get the equation：
 4A + 3B + 3C + 5D + 3E = 21    (1)
 
9
4
B + 
13
4
C + 
3
4
D = 
3166
11
    (2)
 2C -2D = 
818
11
    (3)
 
19
9
D = 
988
33
    (4)
- 
22
19
E = 
2054
19
    (5)

Multiply both sides of equation (5) by 57
Divide both sides of equation (5) by 22, get the equation：
        -3E = 
3081
11
    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 4A + 3B + 3C + 5D = 
3312
11
    (1)
 
9
4
B + 
13
4
C + 
3
4
D = 
3166
11
    (2)
 2C -2D = 
818
11
    (3)
 
19
9
D = 
988
33
    (4)
- 
22
19
E = 
2054
19
    (5)

Multiply both sides of equation (4) by 18
Divide both sides of equation (4) by 19, get the equation：
         2D = 
312
11
    (16)
, then add the two sides of equation (16) to both sides of equation (3), get the equation：
 4A + 3B + 3C + 5D = 
3312
11
    (1)
 
9
4
B + 
13
4
C + 
3
4
D = 
3166
11
    (2)
 2C = 
1130
11
    (3)
 
19
9
D = 
988
33
    (4)
 E = - 
1027
11
    (5)

Multiply both sides of equation (4) by 27
Divide both sides of equation (4) by 76, get the equation：
         
3
4
D = 
117
11
    (17)
, then subtract both sides of equation (17) from both sides of equation (2), get the equation：
 4A + 3B + 3C + 5D = 
3312
11
    (1)
 
9
4
B + 
13
4
C = 
3049
11
    (2)
 2C = 
1130
11
    (3)
 
19
9
D = 
988
33
    (4)
 E = - 
1027
11
    (5)

Multiply both sides of equation (4) by 45
Divide both sides of equation (4) by 19, get the equation：
         5D = 
780
11
    (18)
, then subtract both sides of equation (18) from both sides of equation (1), get the equation：
 4A + 3B + 3C = 
2532
11
    (1)
 
9
4
B + 
13
4
C = 
3049
11
    (2)
 2C = 
1130
11
    (3)
 
19
9
D = 
988
33
    (4)
 E = - 
1027
11
    (5)

Multiply both sides of equation (3) by 13
Divide both sides of equation (3) by 8, get the equation：
         
13
4
C = 
7345
44
    (19)
, then subtract both sides of equation (19) from both sides of equation (2), get the equation：
 4A + 3B + 3C = 
2532
11
    (1)
 
9
4
B = 
441
4
    (2)
 2C = 
1130
11
    (3)
 D = 
156
11
    (4)
 E = - 
1027
11
    (5)

Multiply both sides of equation (3) by 3
Divide both sides of equation (3) by 2, get the equation：
         3C = 
1695
11
    (20)
, then subtract both sides of equation (20) from both sides of equation (1), get the equation：
 4A + 3B = 
837
11
    (1)
 
9
4
B = 
441
4
    (2)
 2C = 
1130
11
    (3)
 D = 
156
11
    (4)
 E = - 
1027
11
    (5)

Multiply both sides of equation (2) by 4
Divide both sides of equation (2) by 3, get the equation：
         3B = 147    (21)
, then subtract both sides of equation (21) from both sides of equation (1), get the equation：
 4A = - 
780
11
    (1)
 
9
4
B = 
441
4
    (2)
 C = 
565
11
    (3)
 D = 
156
11
    (4)
 E = - 
1027
11
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = - 
195
11
    (1)
 B = 49    (2)
 C = 
565
11
    (3)
 D = 
156
11
    (4)
 E = - 
1027
11
    (5)


Therefore, the solution of the equation set is:
A = - 
195
11
B = 49
C = 
565
11
D = 
156
11
E = - 
1027
11


Convert the solution of the equation set to decimals:
A = -17.727273
B = 49
C = 51.363636
D = 14.181818
E = -93.363636

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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