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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:
 A + B + C + D = 1    (1)
 37A -27B = 0    (2)
 27A -37B + 36C = 0    (3)
 9A + 9B -40C + 48D = 0    (4)
Question solving process:

Multiply both sides of equation (1) by 37, the equation can be obtained:
         37A + 37B + 37C + 37D = 37    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 A + B + C + D = 1    (1)
-64B -37C -37D = -37    (2)
 27A -37B + 36C = 0    (3)
 9A + 9B -40C + 48D = 0    (4)

Multiply both sides of equation (1) by 27, the equation can be obtained:
         27A + 27B + 27C + 27D = 27    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 A + B + C + D = 1    (1)
-64B -37C -37D = -37    (2)
-64B + 9C -27D = -27    (3)
 9A + 9B -40C + 48D = 0    (4)

Multiply both sides of equation (1) by 9, the equation can be obtained:
         9A + 9B + 9C + 9D = 9    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 A + B + C + D = 1    (1)
-64B -37C -37D = -37    (2)
-64B + 9C -27D = -27    (3)
-49C + 39D = -9    (4)

Subtract both sides of equation (2) from both sides of equation (3) ,the equations are reduced to:
 A + B + C + D = 1    (1)
-64B -37C -37D = -37    (2)
 46C + 10D = 10    (3)
-49C + 39D = -9    (4)

Multiply both sides of equation (3) by 49
Divide the two sides of equation (3) by 46, the equation can be obtained:
         49C + 
245
23
D = 
245
23
    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 A + B + C + D = 1    (1)
-64B -37C -37D = -37    (2)
 46C + 10D = 10    (3)
 
1142
23
D = 
38
23
    (4)

Multiply both sides of equation (4) by 115
Divide both sides of equation (4) by 571, get the equation：
         
5710
571
D = 
190
571
    (9)
, then subtract both sides of equation (9) from both sides of equation (3), get the equation：
 A + B + C + D = 1    (1)
-64B -37C -37D = -37    (2)
 46C = 
5520
571
    (3)
 
1142
23
D = 
38
23
    (4)

Multiply both sides of equation (4) by 851
Divide both sides of equation (4) by 1142, get the equation：
         
21127
571
D = 
703
571
    (10)
, then add the two sides of equation (10) to both sides of equation (2), get the equation：
 A + B + C + D = 1    (1)
-64B -37C = - 
20424
571
    (2)
 46C = 
5520
571
    (3)
 
1142
23
D = 
38
23
    (4)

Multiply both sides of equation (4) by 23
Divide both sides of equation (4) by 1142, get the equation：
         D = 
19
571
    (11)
, then subtract both sides of equation (11) from both sides of equation (1), get the equation：
 A + B + C = 
552
571
    (1)
-64B -37C = - 
20424
571
    (2)
 46C = 
5520
571
    (3)
 
1142
23
D = 
38
23
    (4)

Multiply both sides of equation (3) by 37
Divide both sides of equation (3) by 46, get the equation：
         37C = 
4440
571
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 A + B + C = 
552
571
    (1)
-64B = - 
15984
571
    (2)
 46C = 
5520
571
    (3)
 D = 
19
571
    (4)

Divide both sides of equation (3) by 46, get the equation：
         C = 
120
571
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 A + B = 
246672
326041
    (1)
-64B = - 
15984
571
    (2)
 46C = 
5520
571
    (3)
 D = 
19
571
    (4)

Divide both sides of equation (2) by 64, get the equation：
        -1B = - 
999
2284
    (14)
, then add the two sides of equation (14) to both sides of equation (1), get the equation：
 A = 
729
2284
    (1)
-64B = - 
15984
571
    (2)
 C = 
120
571
    (3)
 D = 
19
571
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
729
2284
    (1)
 B = 
999
2284
    (2)
 C = 
120
571
    (3)
 D = 
19
571
    (4)


Therefore, the solution of the equation set is:
A = 
729
2284
B = 
999
2284
C = 
120
571
D = 
19
571


Convert the solution of the equation set to decimals:
A = 0.319177
B = 0.437391
C = 0.210158
D = 0.033275

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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