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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:
 90A + 100B + 75C + 60D = 90    (1)
 120A + 135B + 95C + 70D = 115    (2)
 135A + 90B + 125C + 100D = 120    (3)
 130A + 135B + 125C + 115D = 130    (4)
Question solving process:

Multiply both sides of equation (1) by 4
Divide the two sides of equation (1) by 3, the equation can be obtained:
         120A + 
400
3
B + 100C + 80D = 120    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 90A + 100B + 75C + 60D = 90    (1)
 
5
3
B -5C -10D = -5    (2)
 135A + 90B + 125C + 100D = 120    (3)
 130A + 135B + 125C + 115D = 130    (4)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 2, the equation can be obtained:
         135A + 150B + 
225
2
C + 90D = 135    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 90A + 100B + 75C + 60D = 90    (1)
 
5
3
B -5C -10D = -5    (2)
-60B + 
25
2
C + 10D = -15    (3)
 130A + 135B + 125C + 115D = 130    (4)

Multiply both sides of equation (1) by 13
Divide the two sides of equation (1) by 9, the equation can be obtained:
         130A + 
1300
9
B + 
325
3
C + 
260
3
D = 130    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 90A + 100B + 75C + 60D = 90    (1)
 
5
3
B -5C -10D = -5    (2)
-60B + 
25
2
C + 10D = -15    (3)
- 
85
9
B + 
50
3
C + 
85
3
D = 0    (4)

Multiply both sides of equation (2) by 36, the equation can be obtained:
         60B -180C -360D = -180    (8)
, then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
 90A + 100B + 75C + 60D = 90    (1)
 
5
3
B -5C -10D = -5    (2)
- 
335
2
C -350D = -195    (3)
- 
85
9
B + 
50
3
C + 
85
3
D = 0    (4)

Multiply both sides of equation (2) by 17
Divide the two sides of equation (2) by 3, the equation can be obtained:
         
85
9
B - 
85
3
C - 
170
3
D = - 
85
3
    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 90A + 100B + 75C + 60D = 90    (1)
 
5
3
B -5C -10D = -5    (2)
- 
335
2
C -350D = -195    (3)
- 
35
3
C - 
85
3
D = - 
85
3
    (4)

Multiply both sides of equation (3) by 14
Divide the two sides of equation (3) by 201, the equation can be obtained:
        - 
2345
201
C - 
4900
201
D = - 
910
67
    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 90A + 100B + 75C + 60D = 90    (1)
 
5
3
B -5C -10D = -5    (2)
- 
335
2
C -350D = -195    (3)
- 
265
67
D = - 
2965
201
    (4)

Multiply both sides of equation (4) by 4690
Divide both sides of equation (4) by 53, get the equation：
        -350D = - 
207550
159
    (11)
, then subtract both sides of equation (11) from both sides of equation (3), get the equation：
 90A + 100B + 75C + 60D = 90    (1)
 
5
3
B -5C -10D = -5    (2)
- 
335
2
C = 
176545
159
    (3)
- 
265
67
D = - 
2965
201
    (4)

Multiply both sides of equation (4) by 134
Divide both sides of equation (4) by 53, get the equation：
        -10D = - 
5930
159
    (12)
, then subtract both sides of equation (12) from both sides of equation (2), get the equation：
 90A + 100B + 75C + 60D = 90    (1)
 
5
3
B -5C = 
5135
159
    (2)
- 
335
2
C = 
176545
159
    (3)
- 
265
67
D = - 
2965
201
    (4)

Multiply both sides of equation (4) by 804
Divide both sides of equation (4) by 53, get the equation：
        -60D = - 
11860
53
    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 90A + 100B + 75C = - 
7090
53
    (1)
 
5
3
B -5C = 
5135
159
    (2)
- 
335
2
C = 
176545
159
    (3)
- 
265
67
D = - 
2965
201
    (4)

Multiply both sides of equation (3) by 2
Divide both sides of equation (3) by 67, get the equation：
        -5C = 
5270
159
    (14)
, then subtract both sides of equation (14) from both sides of equation (2), get the equation：
 90A + 100B + 75C = - 
7090
53
    (1)
 
5
3
B = - 
45
53
    (2)
- 
335
2
C = 
176545
159
    (3)
 D = 
593
159
    (4)

Multiply both sides of equation (3) by 30
Divide both sides of equation (3) by 67, get the equation：
        -75C = 
26350
53
    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 90A + 100B = 
19260
53
    (1)
 
5
3
B = - 
45
53
    (2)
- 
335
2
C = 
176545
159
    (3)
 D = 
593
159
    (4)

Multiply both sides of equation (2) by 60, get the equation：
         100B = - 
2700
53
    (16)
, then subtract both sides of equation (16) from both sides of equation (1), get the equation：
 90A = 
21960
53
    (1)
 
5
3
B = - 
45
53
    (2)
 C = - 
1054
159
    (3)
 D = 
593
159
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
244
53
    (1)
 B = - 
27
53
    (2)
 C = - 
1054
159
    (3)
 D = 
593
159
    (4)


Therefore, the solution of the equation set is:
A = 
244
53
B = - 
27
53
C = - 
1054
159
D = 
593
159


Convert the solution of the equation set to decimals:
A = 4.603774
B = -0.509434
C = -6.628931
D = 3.729560

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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