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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)
 135A + 90B + 125C + 100D = 120    (2)
 130A + 135B + 125C + 115D = 130    (3)
 150A + 130B + 115C + 135D = 135    (4)
Question solving process:

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    (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)
-60B + 
25
2
C + 10D = -15    (2)
 130A + 135B + 125C + 115D = 130    (3)
 150A + 130B + 115C + 135D = 135    (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    (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)
-60B + 
25
2
C + 10D = -15    (2)
- 
85
9
B + 
50
3
C + 
85
3
D = 0    (3)
 150A + 130B + 115C + 135D = 135    (4)

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 3, the equation can be obtained:
         150A + 
500
3
B + 125C + 100D = 150    (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)
-60B + 
25
2
C + 10D = -15    (2)
- 
85
9
B + 
50
3
C + 
85
3
D = 0    (3)
- 
110
3
B -10C + 35D = -15    (4)

Multiply both sides of equation (2) by 17
Divide the two sides of equation (2) by 108, the equation can be obtained:
        - 
85
9
B + 
425
216
C + 
85
54
D = - 
85
36
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
 90A + 100B + 75C + 60D = 90    (1)
-60B + 
25
2
C + 10D = -15    (2)
 
3175
216
C + 
1445
54
D = 
85
36
    (3)
- 
110
3
B -10C + 35D = -15    (4)

Multiply both sides of equation (2) by 11
Divide the two sides of equation (2) by 18, the equation can be obtained:
        - 
110
3
B + 
275
36
C + 
55
9
D = - 
55
6
    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 90A + 100B + 75C + 60D = 90    (1)
-60B + 
25
2
C + 10D = -15    (2)
 
3175
216
C + 
1445
54
D = 
85
36
    (3)
- 
635
36
C + 
260
9
D = - 
35
6
    (4)

Multiply both sides of equation (3) by 762
Divide the two sides of equation (3) by 635, the equation can be obtained:
         
80645
4572
C + 
36703
1143
D = 
2159
762
    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 90A + 100B + 75C + 60D = 90    (1)
-60B + 
25
2
C + 10D = -15    (2)
 
3175
216
C + 
1445
54
D = 
85
36
    (3)
 
7747
127
D = - 
381
127
    (4)

Multiply both sides of equation (4) by 183515
Divide both sides of equation (4) by 418338, get the equation：
         
183515
6858
D = - 
1445
1098
    (11)
, then subtract both sides of equation (11) from both sides of equation (3), get the equation：
 90A + 100B + 75C + 60D = 90    (1)
-60B + 
25
2
C + 10D = -15    (2)
 
3175
216
C = 
8075
2196
    (3)
 
7747
127
D = - 
381
127
    (4)

Multiply both sides of equation (4) by 1270
Divide both sides of equation (4) by 7747, get the equation：
         
1270
127
D = - 
3810
7747
    (12)
, then subtract both sides of equation (12) from both sides of equation (2), get the equation：
 90A + 100B + 75C + 60D = 90    (1)
-60B + 
25
2
C = - 
112395
7747
    (2)
 
3175
216
C = 
8075
2196
    (3)
 
7747
127
D = - 
381
127
    (4)

Multiply both sides of equation (4) by 7620
Divide both sides of equation (4) by 7747, get the equation：
         
7620
127
D = - 
22860
7747
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 90A + 100B + 75C = 
720090
7747
    (1)
-60B + 
25
2
C = - 
112395
7747
    (2)
 
3175
216
C = 
8075
2196
    (3)
 
7747
127
D = - 
381
127
    (4)

Multiply both sides of equation (3) by 108
Divide both sides of equation (3) by 127, get the equation：
         
3175
254
C = 
24225
7747
    (14)
, then subtract both sides of equation (14) from both sides of equation (2), get the equation：
 90A + 100B + 75C = 
720090
7747
    (1)
-60B = - 
136620
7747
    (2)
 
3175
216
C = 
8075
2196
    (3)
 D = - 
381
7747
    (4)

Multiply both sides of equation (3) by 648
Divide both sides of equation (3) by 127, get the equation：
         
9525
127
C = 
145350
7747
    (15)
, then subtract both sides of equation (15) from both sides of equation (1), get the equation：
 90A + 100B = 
574740
7747
    (1)
-60B = - 
136620
7747
    (2)
 
3175
216
C = 
8075
2196
    (3)
 D = - 
381
7747
    (4)

Multiply both sides of equation (2) by 5
Divide both sides of equation (2) by 3, get the equation：
        -100B = - 
227700
7747
    (16)
, then add the two sides of equation (16) to both sides of equation (1), get the equation：
 90A = 
347040
7747
    (1)
-60B = - 
136620
7747
    (2)
 C = 
1938
7747
    (3)
 D = - 
381
7747
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
3856
7747
    (1)
 B = 
2277
7747
    (2)
 C = 
1938
7747
    (3)
 D = - 
381
7747
    (4)


Therefore, the solution of the equation set is:
A = 
3856
7747
B = 
2277
7747
C = 
1938
7747
D = - 
381
7747


Convert the solution of the equation set to decimals:
A = 0.497741
B = 0.293920
C = 0.250161
D = -0.049180

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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