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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 + 3C = 8    (1)
 B + 3D = 9    (2)
 C + 3E = 10    (3)
 3A + D = 11    (4)
 3B + E = 12    (5)
Question solving process:

Multiply both sides of equation (1) by 3, the equation can be obtained:
         3A + 9C = 24    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 A + 3C = 8    (1)
 B + 3D = 9    (2)
 C + 3E = 10    (3)
-9C + D = -13    (4)
 3B + E = 12    (5)

Multiply both sides of equation (2) by 3, the equation can be obtained:
         3B + 9D = 27    (7)
, then subtract both sides of equation (7) from both sides of equation (5), the equations are reduced to:
 A + 3C = 8    (1)
 B + 3D = 9    (2)
 C + 3E = 10    (3)
-9C + D = -13    (4)
-9D + E = -15    (5)

Multiply both sides of equation (3) by 9, the equation can be obtained:
         9C + 27E = 90    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 A + 3C = 8    (1)
 B + 3D = 9    (2)
 C + 3E = 10    (3)
 D + 27E = 77    (4)
-9D + E = -15    (5)

Multiply both sides of equation (4) by 9, the equation can be obtained:
         9D + 243E = 693    (9)
, then add the two sides of equation (9) to both sides of equation (5), the equations are reduced to:
 A + 3C = 8    (1)
 B + 3D = 9    (2)
 C + 3E = 10    (3)
 D + 27E = 77    (4)
 244E = 678    (5)

Multiply both sides of equation (5) by 27
Divide both sides of equation (5) by 244, get the equation：
         27E = 
9153
122
    (10)
, then subtract both sides of equation (10) from both sides of equation (4), get the equation：
 A + 3C = 8    (1)
 B + 3D = 9    (2)
 C + 3E = 10    (3)
 D = 
241
122
    (4)
 244E = 678    (5)

Multiply both sides of equation (5) by 3
Divide both sides of equation (5) by 244, get the equation：
         3E = 
1017
122
    (11)
, then subtract both sides of equation (11) from both sides of equation (3), get the equation：
 A + 3C = 8    (1)
 B + 3D = 9    (2)
 C = 
203
122
    (3)
 D = 
241
122
    (4)
 244E = 678    (5)

Multiply both sides of equation (4) by 3, get the equation：
         3D = 
723
122
    (12)
, then subtract both sides of equation (12) from both sides of equation (2), get the equation：
 A + 3C = 8    (1)
 B = 
375
122
    (2)
 C = 
203
122
    (3)
 D = 
241
122
    (4)
 E = 
339
122
    (5)

Multiply both sides of equation (3) by 3, get the equation：
         3C = 
609
122
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 A = 
367
122
    (1)
 B = 
375
122
    (2)
 C = 
203
122
    (3)
 D = 
241
122
    (4)
 E = 
339
122
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
367
122
    (1)
 B = 
375
122
    (2)
 C = 
203
122
    (3)
 D = 
241
122
    (4)
 E = 
339
122
    (5)


Therefore, the solution of the equation set is:
A = 
367
122
B = 
375
122
C = 
203
122
D = 
241
122
E = 
339
122


Convert the solution of the equation set to decimals:
A = 3.008197
B = 3.073770
C = 1.663934
D = 1.975410
E = 2.778689

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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