Mathematics
         
语言:中文    Language:English
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:
 36A + 8D = 2000    (1)
 34B + 7D = 2000    (2)
 24C + 5D = 1700    (3)
 7A + 7B + 7C + 19D = 2000    (4)
Question solving process:

Multiply both sides of equation (1) by 7
Divide the two sides of equation (1) by 36, the equation can be obtained:
         7A + 
14
9
D = 
3500
9
    (5)
, then subtract both sides of equation (5) from both sides of equation (4), the equations are reduced to:
 36A + 8D = 2000    (1)
 34B + 7D = 2000    (2)
 24C + 5D = 1700    (3)
 7B + 7C + 
157
9
D = 
14500
9
    (4)

Multiply both sides of equation (2) by 7
Divide the two sides of equation (2) by 34, the equation can be obtained:
         7B + 
49
34
D = 
7000
17
    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 36A + 8D = 2000    (1)
 34B + 7D = 2000    (2)
 24C + 5D = 1700    (3)
 7C + 
4897
306
D = 
183500
153
    (4)

Multiply both sides of equation (3) by 7
Divide the two sides of equation (3) by 24, the equation can be obtained:
         7C + 
35
24
D = 
2975
6
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 36A + 8D = 2000    (1)
 34B + 7D = 2000    (2)
 24C + 5D = 1700    (3)
 
17803
1224
D = 
215275
306
    (4)

Multiply both sides of equation (4) by 6120
Divide both sides of equation (4) by 17803, get the equation:
         
4685
937
D = 
4305500
17803
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), get the equation:
 36A + 8D = 2000    (1)
 34B + 7D = 2000    (2)
 24C = 
25959600
17803
    (3)
 
17803
1224
D = 
215275
306
    (4)

Multiply both sides of equation (4) by 8568
Divide both sides of equation (4) by 17803, get the equation:
         
6559
937
D = 
6027700
17803
    (9)
, then subtract both sides of equation (9) from both sides of equation (2), get the equation:
 36A + 8D = 2000    (1)
 34B = 
29578300
17803
    (2)
 24C = 
25959600
17803
    (3)
 
17803
1224
D = 
215275
306
    (4)

Multiply both sides of equation (4) by 9792
Divide both sides of equation (4) by 17803, get the equation:
         
7496
937
D = 
6888800
17803
    (10)
, then subtract both sides of equation (10) from both sides of equation (1), get the equation:
 36A = 
28717200
17803
    (1)
 34B = 
29578300
17803
    (2)
 24C = 
25959600
17803
    (3)
 
17803
1224
D = 
215275
306
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A = 
797700
17803
    (1)
 B = 
869950
17803
    (2)
 C = 
1081650
17803
    (3)
 D = 
861100
17803
    (4)


Therefore, the solution of the equation set is:
A = 
797700
17803
B = 
869950
17803
C = 
1081650
17803
D = 
861100
17803


Convert the solution of the equation set to decimals:
A = 44.807055
B = 48.865360
C = 60.756614
D = 48.368253

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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