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:
 70A + 9D = 1146    (1)
 64B + 10D = 5260    (2)
 61C + 12D = 4450    (3)
 16A + 16B + 16C + 60D = 8000    (4)
Question solving process:

Multiply both sides of equation (1) by 8
Divide the two sides of equation (1) by 35, the equation can be obtained:
         16A + 
72
35
D = 
9168
35
    (5)
, then subtract both sides of equation (5) from both sides of equation (4), the equations are reduced to:
 70A + 9D = 1146    (1)
 64B + 10D = 5260    (2)
 61C + 12D = 4450    (3)
 16B + 16C + 
2028
35
D = 
270832
35
    (4)

Divide the two sides of equation (2) by 4, the equation can be obtained:
         16B + 
5
2
D = 1315    (6)
, then subtract both sides of equation (6) from both sides of equation (4), the equations are reduced to:
 70A + 9D = 1146    (1)
 64B + 10D = 5260    (2)
 61C + 12D = 4450    (3)
 16C + 
3881
70
D = 
224807
35
    (4)

Multiply both sides of equation (3) by 16
Divide the two sides of equation (3) by 61, the equation can be obtained:
         16C + 
192
61
D = 
71200
61
    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 70A + 9D = 1146    (1)
 64B + 10D = 5260    (2)
 61C + 12D = 4450    (3)
 
223301
4270
D = 
11221227
2135
    (4)

Multiply both sides of equation (4) by 51240
Divide both sides of equation (4) by 223301, get the equation:
         
2316
193
D = 
269309448
223301
    (8)
, then subtract both sides of equation (8) from both sides of equation (3), get the equation:
 70A + 9D = 1146    (1)
 64B + 10D = 5260    (2)
 61C = 
724380002
223301
    (3)
 
223301
4270
D = 
11221227
2135
    (4)

Multiply both sides of equation (4) by 42700
Divide both sides of equation (4) by 223301, get the equation:
         
1930
193
D = 
224424540
223301
    (9)
, then subtract both sides of equation (9) from both sides of equation (2), get the equation:
 70A + 9D = 1146    (1)
 64B = 
950138720
223301
    (2)
 61C = 
724380002
223301
    (3)
 
223301
4270
D = 
11221227
2135
    (4)

Multiply both sides of equation (4) by 38430
Divide both sides of equation (4) by 223301, get the equation:
         
1737
193
D = 
201982086
223301
    (10)
, then subtract both sides of equation (10) from both sides of equation (1), get the equation:
 70A = 
53920860
223301
    (1)
 64B = 
950138720
223301
    (2)
 61C = 
724380002
223301
    (3)
 
223301
4270
D = 
11221227
2135
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A = 
770298
223301
    (1)
 B = 
29691835
446602
    (2)
 C = 
11875082
223301
    (3)
 D = 
22442454
223301
    (4)


Therefore, the solution of the equation set is:
A = 
770298
223301
B = 
29691835
446602
C = 
11875082
223301
D = 
22442454
223301


Convert the solution of the equation set to decimals:
A = 3.449595
B = 66.483883
C = 53.179708
D = 100.503150

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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