Mathematics
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current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 2C -2E = 6    (1)
 2A -3F = 3    (2)
 2B -1D = 2    (3)
 A -1C + D -1E = 0    (4)
 A -1B + E -1F = 0    (5)
 2C + D + 3F = 11    (6)
Question solving process:

交After the exchange of equation (1) and equation (2)， the equation system becomes:
 2A -3F = 3    (1)
 2C -2E = 6    (2)
 2B -1D = 2    (3)
 A -1C + D -1E = 0    (4)
 A -1B + E -1F = 0    (5)
 2C + D + 3F = 11    (6)

Divide the two sides of equation (1) by 2, the equation can be obtained:
         A - 
3
2
F = 
3
2
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 2A -3F = 3    (1)
 2C -2E = 6    (2)
 2B -1D = 2    (3)
-1C + D -1E + 
3
2
F = - 
3
2
    (4)
 A -1B + E -1F = 0    (5)
 2C + D + 3F = 11    (6)

Divide the two sides of equation (1) by 2, the equation can be obtained:
         A - 
3
2
F = 
3
2
    (8)
, then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
 2A -3F = 3    (1)
 2C -2E = 6    (2)
 2B -1D = 2    (3)
-1C + D -1E + 
3
2
F = - 
3
2
    (4)
-1B + E + 
1
2
F = - 
3
2
    (5)
 2C + D + 3F = 11    (6)

交After the exchange of equation (2) and equation (3)， the equation system becomes:
 2A -3F = 3    (1)
 2B -1D = 2    (2)
 2C -2E = 6    (3)
-1C + D -1E + 
3
2
F = - 
3
2
    (4)
-1B + E + 
1
2
F = - 
3
2
    (5)
 2C + D + 3F = 11    (6)

Divide the two sides of equation (2) by 2, the equation can be obtained:
         B - 
1
2
D = 1    (9)
, then add the two sides of equation (9) to both sides of equation (5), the equations are reduced to:
 2A -3F = 3    (1)
 2B -1D = 2    (2)
 2C -2E = 6    (3)
-1C + D -1E + 
3
2
F = - 
3
2
    (4)
- 
1
2
D + E + 
1
2
F = - 
1
2
    (5)
 2C + D + 3F = 11    (6)

Divide the two sides of equation (3) by 2, the equation can be obtained:
         C -1E = 3    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 2A -3F = 3    (1)
 2B -1D = 2    (2)
 2C -2E = 6    (3)
 D -2E + 
3
2
F = 
3
2
    (4)
- 
1
2
D + E + 
1
2
F = - 
1
2
    (5)
 2C + D + 3F = 11    (6)

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

Divide the two sides of equation (4) by 2, the equation can be obtained:
         
1
2
D -1E + 
3
4
F = 
3
4
    (11)
, then add the two sides of equation (11) to both sides of equation (5), the equations are reduced to:
 2A -3F = 3    (1)
 2B -1D = 2    (2)
 2C -2E = 6    (3)
 D -2E + 
3
2
F = 
3
2
    (4)
 
5
4
F = 
1
4
    (5)
 D + 2E + 3F = 5    (6)

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

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

Multiply both sides of equation (6) by 6
Divide both sides of equation (6) by 5, get the equation：
         
3
2
F = 
3
10
    (12)
, then subtract both sides of equation (12) from both sides of equation (5), get the equation：
 2A -3F = 3    (1)
 2B -1D = 2    (2)
 2C -2E = 6    (3)
 D -2E + 
3
2
F = 
3
2
    (4)
 4E = 
16
5
    (5)
 
5
4
F = 
1
4
    (6)

Multiply both sides of equation (6) by 6
Divide both sides of equation (6) by 5, get the equation：
         
3
2
F = 
3
10
    (13)
, then subtract both sides of equation (13) from both sides of equation (4), get the equation：
 2A -3F = 3    (1)
 2B -1D = 2    (2)
 2C -2E = 6    (3)
 D -2E = 
6
5
    (4)
 4E = 
16
5
    (5)
 
5
4
F = 
1
4
    (6)

Multiply both sides of equation (6) by 12
Divide both sides of equation (6) by 5, get the equation：
         3F = 
3
5
    (14)
, then add the two sides of equation (14) to both sides of equation (1), get the equation：
 2A = 
18
5
    (1)
 2B -1D = 2    (2)
 2C -2E = 6    (3)
 D -2E = 
6
5
    (4)
 4E = 
16
5
    (5)
 
5
4
F = 
1
4
    (6)

Divide both sides of equation (5) by 2, get the equation：
         2E = 
8
5
    (15)
, then add the two sides of equation (15) to both sides of equation (4), get the equation：
 2A = 
18
5
    (1)
 2B -1D = 2    (2)
 2C -2E = 6    (3)
 D = 
14
5
    (4)
 4E = 
16
5
    (5)
 F = 
1
5
    (6)

Divide both sides of equation (5) by 2, get the equation：
         2E = 
8
5
    (16)
, then add the two sides of equation (16) to both sides of equation (3), get the equation：
 2A = 
18
5
    (1)
 2B -1D = 2    (2)
 2C = 
38
5
    (3)
 D = 
14
5
    (4)
 4E = 
16
5
    (5)
 F = 
1
5
    (6)

Add both sides of equation (4) to both sides of equation (2), get the equation：
 2A = 
18
5
    (1)
 2B = 
24
5
    (2)
 2C = 
38
5
    (3)
 D = 
14
5
    (4)
 E = 
4
5
    (5)
 F = 
1
5
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
9
5
    (1)
 B = 
12
5
    (2)
 C = 
19
5
    (3)
 D = 
14
5
    (4)
 E = 
4
5
    (5)
 F = 
1
5
    (6)


Therefore, the solution of the equation set is:
A = 
9
5
B = 
12
5
C = 
19
5
D = 
14
5
E = 
4
5
F = 
1
5


Convert the solution of the equation set to decimals:
A = 1.800000
B = 2.400000
C = 3.800000
D = 2.800000
E = 0.800000
F = 0.200000

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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