Mathematics
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Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 8A -4C = 4    (1)
 2B + E = 0    (2)
-4A + 4C + D -1E = 0    (3)
 B + 
1
4
D = 0    (4)
 C = 4    (5)
Question solving process:

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

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

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

Multiply both sides of equation (4) by 2, the equation can be obtained:
         
1
2
D -1E = 0    (9)
, then add the two sides of equation (9) to both sides of equation (5), the equations are reduced to:
 8A -4C = 4    (1)
 2B + E = 0    (2)
 2C + D -1E = 2    (3)
 
1
4
D - 
1
2
E = 0    (4)
- 
1
2
E = 3    (5)

Subtract both sides of equation (5) from both sides of equation (4), get the equation：
 8A -4C = 4    (1)
 2B + E = 0    (2)
 2C + D -1E = 2    (3)
 
1
4
D = -3    (4)
- 
1
2
E = 3    (5)

Multiply both sides of equation (5) by 2, get the equation：
        -1E = 6    (10)
, then subtract both sides of equation (10) from both sides of equation (3), get the equation：
 8A -4C = 4    (1)
 2B + E = 0    (2)
 2C + D = -4    (3)
 
1
4
D = -3    (4)
- 
1
2
E = 3    (5)

Multiply both sides of equation (5) by 2, get the equation：
        -1E = 6    (11)
, then add the two sides of equation (11) to both sides of equation (2), get the equation：
 8A -4C = 4    (1)
 2B = 6    (2)
 2C + D = -4    (3)
 
1
4
D = -3    (4)
- 
1
2
E = 3    (5)

Multiply both sides of equation (4) by 4, get the equation：
         D = -12    (12)
, then subtract both sides of equation (12) from both sides of equation (3), get the equation：
 8A -4C = 4    (1)
 2B = 6    (2)
 2C = 8    (3)
 
1
4
D = -3    (4)
 E = -6    (5)

Multiply both sides of equation (3) by 2, get the equation：
         4C = 16    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 8A = 20    (1)
 2B = 6    (2)
 2C = 8    (3)
 D = -12    (4)
 E = -6    (5)

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


Therefore, the solution of the equation set is:
A = 
5
2
B = 3
C = 4
D = -12
E = -6


Convert the solution of the equation set to decimals:
A = 2.500000
B = 3
C = 4
D = -12
E = -6

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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