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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:
 18A + 18B + 18C + D = - 
273658933
50000
    (1)
-6A -6B + 18C + D = - 
273658933
50000
    (2)
-6A + 2B + 2C + D = - 
273658933
50000
    (3)
-2A -6B + 2C + D = - 
273658933
50000
    (4)
Question solving process:

Divide the two sides of equation (1) by 3, the equation can be obtained:
         6A + 6B + 6C + 
1
3
D = - 
273658933
150000
    (5)
, then add the two sides of equation (5) to both sides of equation (2), the equations are reduced to:
 18A + 18B + 18C + D = - 
273658933
50000
    (1)
 24C + 
4
3
D = - 
273658933
37500
    (2)
-6A + 2B + 2C + D = - 
273658933
50000
    (3)
-2A -6B + 2C + D = - 
273658933
50000
    (4)

Divide the two sides of equation (1) by 3, the equation can be obtained:
         6A + 6B + 6C + 
1
3
D = - 
273658933
150000
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 18A + 18B + 18C + D = - 
273658933
50000
    (1)
 24C + 
4
3
D = - 
273658933
37500
    (2)
 8B + 8C + 
4
3
D = - 
273658933
37500
    (3)
-2A -6B + 2C + D = - 
273658933
50000
    (4)

Divide the two sides of equation (1) by 9, the equation can be obtained:
         2A + 2B + 2C + 
1
9
D = - 
273658933
450000
    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 18A + 18B + 18C + D = - 
273658933
50000
    (1)
 24C + 
4
3
D = - 
273658933
37500
    (2)
 8B + 8C + 
4
3
D = - 
273658933
37500
    (3)
-4B + 4C + 
10
9
D = - 
259729661
75000
    (4)

交After the exchange of equation (2) and equation (3)， the equation system becomes:
 18A + 18B + 18C + D = - 
273658933
50000
    (1)
 8B + 8C + 
4
3
D = - 
273658933
37500
    (2)
 24C + 
4
3
D = - 
273658933
37500
    (3)
-4B + 4C + 
10
9
D = - 
259729661
75000
    (4)

Divide the two sides of equation (2) by 2, the equation can be obtained:
         4B + 4C + 
2
3
D = - 
273658933
75000
    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 18A + 18B + 18C + D = - 
273658933
50000
    (1)
 8B + 8C + 
4
3
D = - 
273658933
37500
    (2)
 24C + 
4
3
D = - 
273658933
37500
    (3)
 8C + 
16
9
D = - 
88898099
12500
    (4)

Divide the two sides of equation (3) by 3, the equation can be obtained:
         8C + 
4
9
D = - 
273658933
112500
    (9)
, then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
 18A + 18B + 18C + D = - 
273658933
50000
    (1)
 8B + 8C + 
4
3
D = - 
273658933
37500
    (2)
 24C + 
4
3
D = - 
273658933
37500
    (3)
 
4
3
D = - 
263211979
56250
    (4)

Subtract both sides of equation (4) from both sides of equation (3), get the equation：
 18A + 18B + 18C + D = - 
273658933
50000
    (1)
 8B + 8C + 
4
3
D = - 
273658933
37500
    (2)
 24C = - 
294552841
112500
    (3)
 
4
3
D = - 
263211979
56250
    (4)

Subtract both sides of equation (4) from both sides of equation (2), get the equation：
 18A + 18B + 18C + D = - 
273658933
50000
    (1)
 8B + 8C = - 
294552841
112500
    (2)
 24C = - 
294552841
112500
    (3)
 
4
3
D = - 
263211979
56250
    (4)

Multiply both sides of equation (4) by 3
Divide both sides of equation (4) by 4, get the equation：
         D = - 
263211979
75000
    (10)
, then subtract both sides of equation (10) from both sides of equation (1), get the equation：
 18A + 18B + 18C = - 
294552841
150000
    (1)
 8B + 8C = - 
294552841
112500
    (2)
 24C = - 
294552841
112500
    (3)
 
4
3
D = - 
263211979
56250
    (4)

Divide both sides of equation (3) by 3, get the equation：
         8C = - 
294552841
337500
    (11)
, then subtract both sides of equation (11) from both sides of equation (2), get the equation：
 18A + 18B + 18C = - 
294552841
150000
    (1)
 8B = - 
294552841
168750
    (2)
 24C = - 
294552841
112500
    (3)
 D = - 
263211979
75000
    (4)

Multiply both sides of equation (3) by 3
Divide both sides of equation (3) by 4, get the equation：
         18C = - 
294552841
150000
    (12)
, then subtract both sides of equation (12) from both sides of equation (1), get the equation：
 18A + 18B = 0    (1)
 8B = - 
294552841
168750
    (2)
 24C = - 
294552841
112500
    (3)
 D = - 
263211979
75000
    (4)

Multiply both sides of equation (2) by 9
Divide both sides of equation (2) by 4, get the equation：
         18B = - 
294552841
75000
    (13)
, then subtract both sides of equation (13) from both sides of equation (1), get the equation：
 18A = 
294552841
75000
    (1)
 8B = - 
294552841
168750
    (2)
 C = - 
294552841
2700000
    (3)
 D = - 
263211979
75000
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
294552841
1350000
    (1)
 B = - 
294552841
1350000
    (2)
 C = - 
294552841
2700000
    (3)
 D = - 
263211979
75000
    (4)


Therefore, the solution of the equation set is:
A = 
294552841
1350000
B = - 
294552841
1350000
C = - 
294552841
2700000
D = - 
263211979
75000


Convert the solution of the equation set to decimals:
A = 218.187290
B = -218.187290
C = -109.093645
D = -3509.493053

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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