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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:
 168A + 141B + 132C + D = 168    (1)
 149A + 125B + 113C + D = 162    (2)
 27A + 23B + 22C + D = 63    (3)
 173A + 146B + 137C + D = 171    (4)
Question solving process:

Multiply both sides of equation (1) by 149
Divide the two sides of equation (1) by 168, the equation can be obtained:
         149A + 
7003
56
B + 
1639
14
C + 
149
168
D = 149    (5)
, then subtract both sides of equation (5) from both sides of equation (2), the equations are reduced to:
 168A + 141B + 132C + D = 168    (1)
- 
3
56
B - 
57
14
C + 
19
168
D = 13    (2)
 27A + 23B + 22C + D = 63    (3)
 173A + 146B + 137C + D = 171    (4)

Multiply both sides of equation (1) by 9
Divide the two sides of equation (1) by 56, the equation can be obtained:
         27A + 
1269
56
B + 
297
14
C + 
9
56
D = 27    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 168A + 141B + 132C + D = 168    (1)
- 
3
56
B - 
57
14
C + 
19
168
D = 13    (2)
 
19
56
B + 
11
14
C + 
47
56
D = 36    (3)
 173A + 146B + 137C + D = 171    (4)

Multiply both sides of equation (1) by 173
Divide the two sides of equation (1) by 168, the equation can be obtained:
         173A + 
8131
56
B + 
1903
14
C + 
173
168
D = 173    (7)
, then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
 168A + 141B + 132C + D = 168    (1)
- 
3
56
B - 
57
14
C + 
19
168
D = 13    (2)
 
19
56
B + 
11
14
C + 
47
56
D = 36    (3)
 
45
56
B + 
15
14
C - 
5
168
D = -2    (4)

Multiply both sides of equation (2) by 19
Divide the two sides of equation (2) by 3, the equation can be obtained:
        - 
19
56
B - 
361
14
C + 
361
504
D = 
247
3
    (8)
, then add the two sides of equation (8) to both sides of equation (3), the equations are reduced to:
 168A + 141B + 132C + D = 168    (1)
- 
3
56
B - 
57
14
C + 
19
168
D = 13    (2)
-25C + 
14
9
D = 
355
3
    (3)
 
45
56
B + 
15
14
C - 
5
168
D = -2    (4)

Multiply both sides of equation (2) by 15, the equation can be obtained:
        - 
45
56
B - 
855
14
C + 
95
56
D = 195    (9)
, then add the two sides of equation (9) to both sides of equation (4), the equations are reduced to:
 168A + 141B + 132C + D = 168    (1)
- 
3
56
B - 
57
14
C + 
19
168
D = 13    (2)
-25C + 
14
9
D = 
355
3
    (3)
-60C + 
5
3
D = 193    (4)

Multiply both sides of equation (3) by 12
Divide the two sides of equation (3) by 5, the equation can be obtained:
        -60C + 
56
15
D = 284    (10)
, then subtract both sides of equation (10) from both sides of equation (4), the equations are reduced to:
 168A + 141B + 132C + D = 168    (1)
- 
3
56
B - 
57
14
C + 
19
168
D = 13    (2)
-25C + 
14
9
D = 
355
3
    (3)
- 
31
15
D = -91    (4)

Multiply both sides of equation (4) by 70
Divide both sides of equation (4) by 93, get the equation：
        - 
14
9
D = - 
6370
93
    (11)
, then add the two sides of equation (11) to both sides of equation (3), get the equation：
 168A + 141B + 132C + D = 168    (1)
- 
3
56
B - 
57
14
C + 
19
168
D = 13    (2)
-25C = 
1545
31
    (3)
- 
31
15
D = -91    (4)

Multiply both sides of equation (4) by 95
Divide both sides of equation (4) by 1736, get the equation：
        - 
19
168
D = - 
1235
248
    (12)
, then add the two sides of equation (12) to both sides of equation (2), get the equation：
 168A + 141B + 132C + D = 168    (1)
- 
3
56
B - 
57
14
C = 
1989
248
    (2)
-25C = 
1545
31
    (3)
- 
31
15
D = -91    (4)

Multiply both sides of equation (4) by 15
Divide both sides of equation (4) by 31, get the equation：
        -1D = - 
1365
31
    (13)
, then add the two sides of equation (13) to both sides of equation (1), get the equation：
 168A + 141B + 132C = 
3843
31
    (1)
- 
3
56
B - 
57
14
C = 
1989
248
    (2)
-25C = 
1545
31
    (3)
- 
31
15
D = -91    (4)

Multiply both sides of equation (3) by 57
Divide both sides of equation (3) by 350, get the equation：
        - 
57
14
C = 
17613
2170
    (14)
, then subtract both sides of equation (14) from both sides of equation (2), get the equation：
 168A + 141B + 132C = 
3843
31
    (1)
- 
3
56
B = - 
837
8680
    (2)
-25C = 
1545
31
    (3)
 D = 
1365
31
    (4)

Multiply both sides of equation (3) by 132
Divide both sides of equation (3) by 25, get the equation：
        -132C = 
40788
155
    (15)
, then add the two sides of equation (15) to both sides of equation (1), get the equation：
 168A + 141B = 
60003
155
    (1)
- 
3
56
B = - 
837
8680
    (2)
-25C = 
1545
31
    (3)
 D = 
1365
31
    (4)

Multiply both sides of equation (2) by 2632, get the equation：
        -141B = - 
39339
155
    (16)
, then add the two sides of equation (16) to both sides of equation (1), get the equation：
 168A = 
20664
155
    (1)
- 
3
56
B = - 
837
8680
    (2)
 C = - 
309
155
    (3)
 D = 
1365
31
    (4)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
123
155
    (1)
 B = 
279
155
    (2)
 C = - 
309
155
    (3)
 D = 
1365
31
    (4)


Therefore, the solution of the equation set is:
A = 
123
155
B = 
279
155
C = - 
309
155
D = 
1365
31


Convert the solution of the equation set to decimals:
A = 0.793548
B = 1.800000
C = -1.993548
D = 44.032258

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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