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:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
-1D + E -1F = 0    (3)
-10A + 10B + 4C = -20    (4)
-4C + 8D + 8E = 20    (5)
-10B -8D + 2F = -40    (6)
Question solving process:

Multiply both sides of equation (1) by 10, the equation can be obtained:
         10A + 10B + 10C = 0    (7)
, then add the two sides of equation (7) to both sides of equation (4), the equations are reduced to:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
-1D + E -1F = 0    (3)
 20B + 14C = -20    (4)
-4C + 8D + 8E = 20    (5)
-10B -8D + 2F = -40    (6)

Multiply both sides of equation (2) by 20, the equation can be obtained:
        -20B + 20C + 20D = 0    (8)
, then add the two sides of equation (8) to both sides of equation (4), the equations are reduced to:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
-1D + E -1F = 0    (3)
 34C + 20D = -20    (4)
-4C + 8D + 8E = 20    (5)
-10B -8D + 2F = -40    (6)

Multiply both sides of equation (2) by 10, the equation can be obtained:
        -10B + 10C + 10D = 0    (9)
, then subtract both sides of equation (9) from both sides of equation (6), the equations are reduced to:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
-1D + E -1F = 0    (3)
 34C + 20D = -20    (4)
-4C + 8D + 8E = 20    (5)
-10C -18D + 2F = -40    (6)

交After the exchange of equation (3) and equation (4), the equation system becomes:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
 34C + 20D = -20    (3)
-1D + E -1F = 0    (4)
-4C + 8D + 8E = 20    (5)
-10C -18D + 2F = -40    (6)

Multiply both sides of equation (3) by 2
Divide the two sides of equation (3) by 17, the equation can be obtained:
         4C + 
40
17
D = 
40
17
    (10)
, then add the two sides of equation (10) to both sides of equation (5), the equations are reduced to:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
 34C + 20D = -20    (3)
-1D + E -1F = 0    (4)
 
176
17
D + 8E = 
300
17
    (5)
-10C -18D + 2F = -40    (6)

Multiply both sides of equation (3) by 5
Divide the two sides of equation (3) by 17, the equation can be obtained:
         10C + 
100
17
D = 
100
17
    (11)
, then add the two sides of equation (11) to both sides of equation (6), the equations are reduced to:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
 34C + 20D = -20    (3)
-1D + E -1F = 0    (4)
 
176
17
D + 8E = 
300
17
    (5)
206
17
D + 2F = 
780
17
    (6)

Multiply both sides of equation (4) by 176
Divide the two sides of equation (4) by 17, the equation can be obtained:
        
176
17
D + 
176
17
E 
176
17
F = 0    (12)
, then add the two sides of equation (12) to both sides of equation (5), the equations are reduced to:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
 34C + 20D = -20    (3)
-1D + E -1F = 0    (4)
 
312
17
E 
176
17
F = 
300
17
    (5)
206
17
D + 2F = 
780
17
    (6)

Multiply both sides of equation (4) by 206
Divide the two sides of equation (4) by 17, the equation can be obtained:
        
206
17
D + 
206
17
E 
206
17
F = 0    (13)
, then subtract both sides of equation (13) from both sides of equation (6), the equations are reduced to:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
 34C + 20D = -20    (3)
-1D + E -1F = 0    (4)
 
312
17
E 
176
17
F = 
300
17
    (5)
206
17
E + 
240
17
F = 
780
17
    (6)

Multiply both sides of equation (5) by 103
Divide the two sides of equation (5) by 156, the equation can be obtained:
         
206
17
E 
4532
663
F = 
2575
221
    (14)
, then add the two sides of equation (14) to both sides of equation (6), the equations are reduced to:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
 34C + 20D = -20    (3)
-1D + E -1F = 0    (4)
 
312
17
E 
176
17
F = 
300
17
    (5)
 
284
39
F = 
7565
221
    (6)

Multiply both sides of equation (6) by 1716
Divide both sides of equation (6) by 1207, get the equation:
         
12496
1207
F = 
58740
1207
    (15)
, then add the two sides of equation (15) to both sides of equation (5), get the equation:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
 34C + 20D = -20    (3)
-1D + E -1F = 0    (4)
 
312
17
E = 
37440
1207
    (5)
 
284
39
F = 
7565
221
    (6)

Multiply both sides of equation (6) by 39
Divide both sides of equation (6) by 284, get the equation:
         F = 
1335
284
    (16)
, then add the two sides of equation (16) to both sides of equation (4), get the equation:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
 34C + 20D = -20    (3)
-1D + E = 
1335
284
    (4)
 
312
17
E = 
37440
1207
    (5)
 
284
39
F = 
7565
221
    (6)

Multiply both sides of equation (5) by 17
Divide both sides of equation (5) by 312, get the equation:
         E = 
120
71
    (17)
, then subtract both sides of equation (17) from both sides of equation (4), get the equation:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
 34C + 20D = -20    (3)
-1D = 
855
284
    (4)
 
312
17
E = 
37440
1207
    (5)
 F = 
1335
284
    (6)

Multiply both sides of equation (4) by 20, get the equation:
        -20D = 
4275
71
    (18)
, then add the two sides of equation (18) to both sides of equation (3), get the equation:
 A + B + C = 0    (1)
-1B + C + D = 0    (2)
 34C = 
5695
71
    (3)
-1D = 
855
284
    (4)
 E = 
120
71
    (5)
 F = 
1335
284
    (6)

Add both sides of equation (4) to both sides of equation (2), get the equation:
 A + B + C = 0    (1)
-1B + C = 
855
284
    (2)
 34C = 
5695
71
    (3)
-1D = 
855
284
    (4)
 E = 
120
71
    (5)
 F = 
1335
284
    (6)

Divide both sides of equation (3) by 34, get the equation:
         C = 
335
142
    (19)
, then subtract both sides of equation (19) from both sides of equation (2), get the equation:
 A + B + C = 0    (1)
-1B = 
185
284
    (2)
 34C = 
5695
71
    (3)
 D = 
855
284
    (4)
 E = 
120
71
    (5)
 F = 
1335
284
    (6)

Divide both sides of equation (3) by 34, get the equation:
         C = 
335
142
    (20)
, then subtract both sides of equation (20) from both sides of equation (1), get the equation:
 A + B = 
335
142
    (1)
-1B = 
185
284
    (2)
 34C = 
5695
71
    (3)
 D = 
855
284
    (4)
 E = 
120
71
    (5)
 F = 
1335
284
    (6)

Add both sides of equation (2) to both sides of equation (1), get the equation:
 A = 
485
284
    (1)
-1B = 
185
284
    (2)
 C = 
335
142
    (3)
 D = 
855
284
    (4)
 E = 
120
71
    (5)
 F = 
1335
284
    (6)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 A = 
485
284
    (1)
 B = 
185
284
    (2)
 C = 
335
142
    (3)
 D = 
855
284
    (4)
 E = 
120
71
    (5)
 F = 
1335
284
    (6)


Therefore, the solution of the equation set is:
A = 
485
284
B = 
185
284
C = 
335
142
D = 
855
284
E = 
120
71
F = 
1335
284


Convert the solution of the equation set to decimals:
A = 1.707746
B = 0.651408
C = -2.359155
D = 3.010563
E = -1.690141
F = -4.700704

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