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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:
 4A + 6C = 0    (1)
 3D -2E = 10    (2)
 4A -1B + 2E = 5    (3)
 A -1B -1C = 0    (4)
-1C + D + E = 0    (5)
Question solving process:

Subtract both sides of equation (1) from both sides of equation (3) ,the equations are reduced to:
 4A + 6C = 0    (1)
 3D -2E = 10    (2)
-1B -6C + 2E = 5    (3)
 A -1B -1C = 0    (4)
-1C + D + E = 0    (5)

Divide the two sides of equation (1) by 4, the equation can be obtained:
         A + 
3
2
C = 0    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 4A + 6C = 0    (1)
 3D -2E = 10    (2)
-1B -6C + 2E = 5    (3)
-1B - 
5
2
C = 0    (4)
-1C + D + E = 0    (5)

交After the exchange of equation (2) and equation (3)， the equation system becomes:
 4A + 6C = 0    (1)
-1B -6C + 2E = 5    (2)
 3D -2E = 10    (3)
-1B - 
5
2
C = 0    (4)
-1C + D + E = 0    (5)

Subtract both sides of equation (2) from both sides of equation (4) ,the equations are reduced to:
 4A + 6C = 0    (1)
-1B -6C + 2E = 5    (2)
 3D -2E = 10    (3)
 
7
2
C -2E = -5    (4)
-1C + D + E = 0    (5)

交After the exchange of equation (3) and equation (4)， the equation system becomes:
 4A + 6C = 0    (1)
-1B -6C + 2E = 5    (2)
 
7
2
C -2E = -5    (3)
 3D -2E = 10    (4)
-1C + D + E = 0    (5)

Multiply both sides of equation (3) by 2
Divide the two sides of equation (3) by 7, the equation can be obtained:
         C - 
4
7
E = - 
10
7
    (7)
, then add the two sides of equation (7) to both sides of equation (5), the equations are reduced to:
 4A + 6C = 0    (1)
-1B -6C + 2E = 5    (2)
 
7
2
C -2E = -5    (3)
 3D -2E = 10    (4)
 D + 
3
7
E = - 
10
7
    (5)

Divide the two sides of equation (4) by 3, the equation can be obtained:
         D - 
2
3
E = 
10
3
    (8)
, then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
 4A + 6C = 0    (1)
-1B -6C + 2E = 5    (2)
 
7
2
C -2E = -5    (3)
 3D -2E = 10    (4)
 
23
21
E = - 
100
21
    (5)

Multiply both sides of equation (5) by 42
Divide both sides of equation (5) by 23, get the equation：
         2E = - 
200
23
    (9)
, then add the two sides of equation (9) to both sides of equation (4), get the equation：
 4A + 6C = 0    (1)
-1B -6C + 2E = 5    (2)
 
7
2
C -2E = -5    (3)
 3D = 
30
23
    (4)
 
23
21
E = - 
100
21
    (5)

Multiply both sides of equation (5) by 42
Divide both sides of equation (5) by 23, get the equation：
         2E = - 
200
23
    (10)
, then add the two sides of equation (10) to both sides of equation (3), get the equation：
 4A + 6C = 0    (1)
-1B -6C + 2E = 5    (2)
 
7
2
C = - 
315
23
    (3)
 3D = 
30
23
    (4)
 
23
21
E = - 
100
21
    (5)

Multiply both sides of equation (5) by 42
Divide both sides of equation (5) by 23, get the equation：
         2E = - 
200
23
    (11)
, then subtract both sides of equation (11) from both sides of equation (2), get the equation：
 4A + 6C = 0    (1)
-1B -6C = 
315
23
    (2)
 
7
2
C = - 
315
23
    (3)
 3D = 
30
23
    (4)
 
23
21
E = - 
100
21
    (5)

Multiply both sides of equation (3) by 12
Divide both sides of equation (3) by 7, get the equation：
         6C = - 
540
23
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 4A + 6C = 0    (1)
-1B = - 
225
23
    (2)
 
7
2
C = - 
315
23
    (3)
 D = 
10
23
    (4)
 E = - 
100
23
    (5)

Multiply both sides of equation (3) by 12
Divide both sides of equation (3) by 7, get the equation：
         6C = - 
540
23
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 4A = 
540
23
    (1)
-1B = - 
225
23
    (2)
 
7
2
C = - 
315
23
    (3)
 D = 
10
23
    (4)
 E = - 
100
23
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
135
23
    (1)
 B = 
225
23
    (2)
 C = - 
90
23
    (3)
 D = 
10
23
    (4)
 E = - 
100
23
    (5)


Therefore, the solution of the equation set is:
A = 
135
23
B = 
225
23
C = - 
90
23
D = 
10
23
E = - 
100
23


Convert the solution of the equation set to decimals:
A = 5.869565
B = 9.782609
C = -3.913043
D = 0.434783
E = -4.347826

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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