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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 = - 
353
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 = - 
353
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 = - 
353
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 = - 
353
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 = - 
2471
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 = - 
353
4
    (2)
 2C -2D + E = -19    (3)
 
25
9
C - 
2
3
D = 
37
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 = - 
353
4
    (2)
 2C -2D + E = -19    (3)
 
19
9
D - 
25
18
E = 
61
2
    (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 = - 
353
4
    (2)
 2C -2D + E = -19    (3)
 
19
9
D - 
25
18
E = 
61
2
    (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 = 
549
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 = - 
353
4
    (2)
 2C -2D + E = -19    (3)
 
19
9
D - 
25
18
E = 
61
2
    (4)
- 
22
19
E = 
892
19
    (5)

Multiply both sides of equation (5) by 475
Divide both sides of equation (5) by 396, get the equation：
        - 
25
18
E = 
5575
99
    (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 = - 
353
4
    (2)
 2C -2D + E = -19    (3)
 
19
9
D = - 
5111
198
    (4)
- 
22
19
E = 
892
19
    (5)

Multiply both sides of equation (5) by 19
Divide both sides of equation (5) by 22, get the equation：
        -1E = 
446
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 = - 
353
4
    (2)
 2C -2D = 
237
11
    (3)
 
19
9
D = - 
5111
198
    (4)
- 
22
19
E = 
892
19
    (5)

Multiply both sides of equation (5) by 171
Divide both sides of equation (5) by 88, get the equation：
        - 
9
4
E = 
2007
22
    (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 = 
131
44
    (2)
 2C -2D = 
237
11
    (3)
 
19
9
D = - 
5111
198
    (4)
- 
22
19
E = 
892
19
    (5)

Multiply both sides of equation (5) by 57
Divide both sides of equation (5) by 22, get the equation：
        -3E = 
1338
11
    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 4A + 3B + 3C + 5D = 
1569
11
    (1)
 
9
4
B + 
13
4
C + 
3
4
D = 
131
44
    (2)
 2C -2D = 
237
11
    (3)
 
19
9
D = - 
5111
198
    (4)
- 
22
19
E = 
892
19
    (5)

Multiply both sides of equation (4) by 18
Divide both sides of equation (4) by 19, get the equation：
         2D = - 
269
11
    (16)
, then add the two sides of equation (16) to both sides of equation (3), get the equation：
 4A + 3B + 3C + 5D = 
1569
11
    (1)
 
9
4
B + 
13
4
C + 
3
4
D = 
131
44
    (2)
 2C = - 
32
11
    (3)
 
19
9
D = - 
5111
198
    (4)
 E = - 
446
11
    (5)

Multiply both sides of equation (4) by 27
Divide both sides of equation (4) by 76, get the equation：
         
3
4
D = - 
807
88
    (17)
, then subtract both sides of equation (17) from both sides of equation (2), get the equation：
 4A + 3B + 3C + 5D = 
1569
11
    (1)
 
9
4
B + 
13
4
C = 
1069
88
    (2)
 2C = - 
32
11
    (3)
 
19
9
D = - 
5111
198
    (4)
 E = - 
446
11
    (5)

Multiply both sides of equation (4) by 45
Divide both sides of equation (4) by 19, get the equation：
         5D = - 
1345
22
    (18)
, then subtract both sides of equation (18) from both sides of equation (1), get the equation：
 4A + 3B + 3C = 
4483
22
    (1)
 
9
4
B + 
13
4
C = 
1069
88
    (2)
 2C = - 
32
11
    (3)
 
19
9
D = - 
5111
198
    (4)
 E = - 
446
11
    (5)

Multiply both sides of equation (3) by 13
Divide both sides of equation (3) by 8, get the equation：
         
13
4
C = - 
52
11
    (19)
, then subtract both sides of equation (19) from both sides of equation (2), get the equation：
 4A + 3B + 3C = 
4483
22
    (1)
 
9
4
B = 
135
8
    (2)
 2C = - 
32
11
    (3)
 D = - 
269
22
    (4)
 E = - 
446
11
    (5)

Multiply both sides of equation (3) by 3
Divide both sides of equation (3) by 2, get the equation：
         3C = - 
48
11
    (20)
, then subtract both sides of equation (20) from both sides of equation (1), get the equation：
 4A + 3B = 
4579
22
    (1)
 
9
4
B = 
135
8
    (2)
 2C = - 
32
11
    (3)
 D = - 
269
22
    (4)
 E = - 
446
11
    (5)

Multiply both sides of equation (2) by 4
Divide both sides of equation (2) by 3, get the equation：
         3B = 
45
2
    (21)
, then subtract both sides of equation (21) from both sides of equation (1), get the equation：
 4A = 
2042
11
    (1)
 
9
4
B = 
135
8
    (2)
 C = - 
16
11
    (3)
 D = - 
269
22
    (4)
 E = - 
446
11
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
1021
22
    (1)
 B = 
15
2
    (2)
 C = - 
16
11
    (3)
 D = - 
269
22
    (4)
 E = - 
446
11
    (5)


Therefore, the solution of the equation set is:
A = 
1021
22
B = 
15
2
C = - 
16
11
D = - 
269
22
E = - 
446
11


Convert the solution of the equation set to decimals:
A = 46.409091
B = 7.500000
C = -1.454545
D = -12.227273
E = -40.545455

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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