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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:
 
12
5
A -5B = 1    (1)
-6A + 6C = 0    (2)
- 
24
5
A + 12D = 0    (3)
-8A + 
239
4
B - 
1
4
C + 
1
4
D = 
216
5
    (4)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 2, the equation can be obtained:
         6A - 
25
2
B = 
5
2
    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
- 
24
5
A + 12D = 0    (3)
-8A + 
239
4
B - 
1
4
C + 
1
4
D = 
216
5
    (4)

Multiply both sides of equation (1) by 2, the equation can be obtained:
         
24
5
A -10B = 2    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
-10B + 12D = 2    (3)
-8A + 
239
4
B - 
1
4
C + 
1
4
D = 
216
5
    (4)

Multiply both sides of equation (1) by 10
Divide the two sides of equation (1) by 3, the equation can be obtained:
         8A - 
50
3
B = 
10
3
    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
-10B + 12D = 2    (3)
 
517
12
B - 
1
4
C + 
1
4
D = 
698
15
    (4)

Multiply both sides of equation (2) by 4
Divide the two sides of equation (2) by 5, the equation can be obtained:
        -10B + 
24
5
C = 2    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
- 
24
5
C + 12D = 0    (3)
 
517
12
B - 
1
4
C + 
1
4
D = 
698
15
    (4)

Multiply both sides of equation (2) by 517
Divide the two sides of equation (2) by 150, the equation can be obtained:
        - 
517
12
B + 
517
25
C = 
517
60
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
- 
24
5
C + 12D = 0    (3)
 
2043
100
C + 
1
4
D = 
1103
20
    (4)

Multiply both sides of equation (3) by 681
Divide the two sides of equation (3) by 160, the equation can be obtained:
        - 
2043
100
C + 
2043
40
D = 0    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
- 
24
5
C + 12D = 0    (3)
 
2053
40
D = 
1103
20
    (4)

Multiply both sides of equation (4) by 480
Divide both sides of equation (4) by 2053, get the equation：
         
24636
2053
D = 
26472
2053
    (11)
, then subtract both sides of equation (11) from both sides of equation (3), get the equation：
 
12
5
A -5B = 1    (1)
- 
25
2
B + 6C = 
5
2
    (2)
- 
24
5
C = - 
26472
2053
    (3)
 
2053
40
D = 
1103
20
    (4)

Multiply both sides of equation (3) by 5
Divide both sides of equation (3) by 4, get the equation：
        -6C = - 
33090
2053
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 
12
5
A -5B = 1    (1)
- 
25
2
B = - 
55915
4106
    (2)
- 
24
5
C = - 
26472
2053
    (3)
 D = 
2206
2053
    (4)

Multiply both sides of equation (2) by 2
Divide both sides of equation (2) by 5, get the equation：
        -5B = - 
11183
2053
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 
12
5
A = 
13236
2053
    (1)
- 
25
2
B = - 
55915
4106
    (2)
 C = 
5515
2053
    (3)
 D = 
2206
2053
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
5515
2053
    (1)
 B = 
11183
10265
    (2)
 C = 
5515
2053
    (3)
 D = 
2206
2053
    (4)


Therefore, the solution of the equation set is:
A = 
5515
2053
B = 
11183
10265
C = 
5515
2053
D = 
2206
2053


Convert the solution of the equation set to decimals:
A = 2.686313
B = 1.089430
C = 2.686313
D = 1.074525

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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