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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:
 2A -5B = 2    (1)
-5A + 6C = 0    (2)
-4A + 12D = 0    (3)
- 
1
4
A + 
239
4
B - 
7
20
C - 
7
20
D = 
433
10
    (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:
         5A - 
25
2
B = 5    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 2A -5B = 2    (1)
- 
25
2
B + 6C = 5    (2)
-4A + 12D = 0    (3)
- 
1
4
A + 
239
4
B - 
7
20
C - 
7
20
D = 
433
10
    (4)

Multiply both sides of equation (1) by 2, the equation can be obtained:
         4A -10B = 4    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 2A -5B = 2    (1)
- 
25
2
B + 6C = 5    (2)
-10B + 12D = 4    (3)
- 
1
4
A + 
239
4
B - 
7
20
C - 
7
20
D = 
433
10
    (4)

Divide the two sides of equation (1) by 8, the equation can be obtained:
         
1
4
A - 
5
8
B = 
1
4
    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 2A -5B = 2    (1)
- 
25
2
B + 6C = 5    (2)
-10B + 12D = 4    (3)
 
473
8
B - 
7
20
C - 
7
20
D = 
871
20
    (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 = 4    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 2A -5B = 2    (1)
- 
25
2
B + 6C = 5    (2)
- 
24
5
C + 12D = 0    (3)
 
473
8
B - 
7
20
C - 
7
20
D = 
871
20
    (4)

Multiply both sides of equation (2) by 473
Divide the two sides of equation (2) by 100, the equation can be obtained:
        - 
473
8
B + 
1419
50
C = 
473
20
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 2A -5B = 2    (1)
- 
25
2
B + 6C = 5    (2)
- 
24
5
C + 12D = 0    (3)
 
2803
100
C - 
7
20
D = 
336
5
    (4)

Multiply both sides of equation (3) by 2803
Divide the two sides of equation (3) by 480, the equation can be obtained:
        - 
2803
100
C + 
2803
40
D = 0    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 2A -5B = 2    (1)
- 
25
2
B + 6C = 5    (2)
- 
24
5
C + 12D = 0    (3)
 
2789
40
D = 
336
5
    (4)

Multiply both sides of equation (4) by 480
Divide both sides of equation (4) by 2789, get the equation：
         
33468
2789
D = 
32256
2789
    (11)
, then subtract both sides of equation (11) from both sides of equation (3), get the equation：
 2A -5B = 2    (1)
- 
25
2
B + 6C = 5    (2)
- 
24
5
C = - 
32256
2789
    (3)
 
2789
40
D = 
336
5
    (4)

Multiply both sides of equation (3) by 5
Divide both sides of equation (3) by 4, get the equation：
        -6C = - 
40320
2789
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 2A -5B = 2    (1)
- 
25
2
B = - 
26375
2789
    (2)
- 
24
5
C = - 
32256
2789
    (3)
 D = 
2688
2789
    (4)

Multiply both sides of equation (2) by 2
Divide both sides of equation (2) by 5, get the equation：
        -5B = - 
10550
2789
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 2A = 
16128
2789
    (1)
- 
25
2
B = - 
26375
2789
    (2)
 C = 
6720
2789
    (3)
 D = 
2688
2789
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
8064
2789
    (1)
 B = 
2110
2789
    (2)
 C = 
6720
2789
    (3)
 D = 
2688
2789
    (4)


Therefore, the solution of the equation set is:
A = 
8064
2789
B = 
2110
2789
C = 
6720
2789
D = 
2688
2789


Convert the solution of the equation set to decimals:
A = 2.891359
B = 0.756544
C = 2.409466
D = 0.963786

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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