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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:
 16A -2B -8C = -2    (1)
-2A + 9B -2C + 
1
10
D = 5    (2)
-80A -20B + 130C -1D = 0    (3)
-1B + C = 3    (4)
Question solving process:

Divide the two sides of equation (1) by 8, the equation can be obtained:
         2A - 
1
4
B -1C = - 
1
4
    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 16A -2B -8C = -2    (1)
 
35
4
B -3C + 
1
10
D = 
19
4
    (2)
-80A -20B + 130C -1D = 0    (3)
-1B + C = 3    (4)

Multiply both sides of equation (1) by 5, the equation can be obtained:
         80A -10B -40C = -10    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 16A -2B -8C = -2    (1)
 
35
4
B -3C + 
1
10
D = 
19
4
    (2)
-30B + 90C -1D = -10    (3)
-1B + C = 3    (4)

Multiply both sides of equation (2) by 24
Divide the two sides of equation (2) by 7, the equation can be obtained:
         30B - 
72
7
C + 
12
35
D = 
114
7
    (7)
, then add the two sides of equation (7) to both sides of equation (3), the equations are reduced to:
 16A -2B -8C = -2    (1)
 
35
4
B -3C + 
1
10
D = 
19
4
    (2)
 
558
7
C - 
23
35
D = 
44
7
    (3)
-1B + C = 3    (4)

Multiply both sides of equation (2) by 4
Divide the two sides of equation (2) by 35, the equation can be obtained:
         B - 
12
35
C + 
2
175
D = 
19
35
    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 16A -2B -8C = -2    (1)
 
35
4
B -3C + 
1
10
D = 
19
4
    (2)
 
558
7
C - 
23
35
D = 
44
7
    (3)
 
23
35
C + 
2
175
D = 
124
35
    (4)

Multiply both sides of equation (3) by 23
Divide the two sides of equation (3) by 2790, the equation can be obtained:
         
23
35
C - 
529
97650
D = 
506
9765
    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 16A -2B -8C = -2    (1)
 
35
4
B -3C + 
1
10
D = 
19
4
    (2)
 
558
7
C - 
23
35
D = 
44
7
    (3)
 
47
2790
D = 
974
279
    (4)

Multiply both sides of equation (4) by 12834
Divide both sides of equation (4) by 329, get the equation：
         
713
1085
D = 
44804
329
    (10)
, then add the two sides of equation (10) to both sides of equation (3), get the equation：
 16A -2B -8C = -2    (1)
 
35
4
B -3C + 
1
10
D = 
19
4
    (2)
 
558
7
C = 
6696
47
    (3)
 
47
2790
D = 
974
279
    (4)

Multiply both sides of equation (4) by 279
Divide both sides of equation (4) by 47, get the equation：
         
1
10
D = 
974
47
    (11)
, then subtract both sides of equation (11) from both sides of equation (2), get the equation：
 16A -2B -8C = -2    (1)
 
35
4
B -3C = - 
3003
188
    (2)
 
558
7
C = 
6696
47
    (3)
 
47
2790
D = 
974
279
    (4)

Multiply both sides of equation (3) by 7
Divide both sides of equation (3) by 186, get the equation：
         3C = 
252
47
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 16A -2B -8C = -2    (1)
 
35
4
B = - 
1995
188
    (2)
 
558
7
C = 
6696
47
    (3)
 D = 
9740
47
    (4)

Multiply both sides of equation (3) by 28
Divide both sides of equation (3) by 279, get the equation：
         8C = 
672
47
    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 16A -2B = 
578
47
    (1)
 
35
4
B = - 
1995
188
    (2)
 
558
7
C = 
6696
47
    (3)
 D = 
9740
47
    (4)

Multiply both sides of equation (2) by 8
Divide both sides of equation (2) by 35, get the equation：
         2B = - 
114
47
    (14)
, then add the two sides of equation (14) to both sides of equation (1), get the equation：
 16A = 
464
47
    (1)
 
35
4
B = - 
1995
188
    (2)
 C = 
84
47
    (3)
 D = 
9740
47
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
29
47
    (1)
 B = - 
57
47
    (2)
 C = 
84
47
    (3)
 D = 
9740
47
    (4)


Therefore, the solution of the equation set is:
A = 
29
47
B = - 
57
47
C = 
84
47
D = 
9740
47


Convert the solution of the equation set to decimals:
A = 0.617021
B = -1.212766
C = 1.787234
D = 207.234043

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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