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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:
 82A + 30B = 1250    (1)
 105B + 15C = 1160    (2)
 15B + 65C + 50D = 990    (3)
 15B + 300D = 995    (4)
Question solving process:

Divide the two sides of equation (2) by 7, the equation can be obtained:
         15B + 
15
7
C = 
1160
7
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 82A + 30B = 1250    (1)
 105B + 15C = 1160    (2)
 
440
7
C + 50D = 
5770
7
    (3)
 15B + 300D = 995    (4)

Divide the two sides of equation (2) by 7, the equation can be obtained:
         15B + 
15
7
C = 
1160
7
    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 82A + 30B = 1250    (1)
 105B + 15C = 1160    (2)
 
440
7
C + 50D = 
5770
7
    (3)
- 
15
7
C + 300D = 
5805
7
    (4)

Multiply both sides of equation (3) by 3
Divide the two sides of equation (3) by 88, the equation can be obtained:
         
15
7
C + 
75
44
D = 
8655
308
    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 82A + 30B = 1250    (1)
 105B + 15C = 1160    (2)
 
440
7
C + 50D = 
5770
7
    (3)
 
13275
44
D = 
37725
44
    (4)

Multiply both sides of equation (4) by 88
Divide both sides of equation (4) by 531, get the equation：
         50D = 
25150
177
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), get the equation：
 82A + 30B = 1250    (1)
 105B + 15C = 1160    (2)
 
440
7
C = 
845240
1239
    (3)
 
13275
44
D = 
37725
44
    (4)

Multiply both sides of equation (3) by 21
Divide both sides of equation (3) by 88, get the equation：
         15C = 
9605
59
    (9)
, then subtract both sides of equation (9) from both sides of equation (2), get the equation：
 82A + 30B = 1250    (1)
 105B = 
58835
59
    (2)
 
440
7
C = 
845240
1239
    (3)
 D = 
503
177
    (4)

Multiply both sides of equation (2) by 2
Divide both sides of equation (2) by 7, get the equation：
         30B = 
16810
59
    (10)
, then subtract both sides of equation (10) from both sides of equation (1), get the equation：
 82A = 
56940
59
    (1)
 105B = 
58835
59
    (2)
 C = 
1921
177
    (3)
 D = 
503
177
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
28470
2419
    (1)
 B = 
1681
177
    (2)
 C = 
1921
177
    (3)
 D = 
503
177
    (4)


Therefore, the solution of the equation set is:
A = 
28470
2419
B = 
1681
177
C = 
1921
177
D = 
503
177


Convert the solution of the equation set to decimals:
A = 11.769326
B = 9.497175
C = 10.853107
D = 2.841808

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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