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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:
 
111
500
x + 
4
125
y + 
629
125
z = 
103
100
    (1)
 
3
100
x + 
3
100
y + 
603
100
z = 1    (2)
 x + 3z = 8    (3)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 37, the equation can be obtained:
         
3
100
x + 
4
925
y + 
17
25
z = 
103
740
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 
111
500
x + 
4
125
y + 
629
125
z = 
103
100
    (1)
 
19
740
y + 
107
20
z = 
637
740
    (2)
 x + 3z = 8    (3)

Multiply both sides of equation (1) by 500
Divide the two sides of equation (1) by 111, the equation can be obtained:
         x + 
16
111
y + 
2516
111
z = 
515
111
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 
111
500
x + 
4
125
y + 
629
125
z = 
103
100
    (1)
 
19
740
y + 
107
20
z = 
637
740
    (2)
- 
16
111
y - 
2183
111
z = 
373
111
    (3)

Multiply both sides of equation (2) by 11840
Divide the two sides of equation (2) by 2109, the equation can be obtained:
         
16
111
y + 
1712
57
z = 
10192
2109
    (6)
, then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
 
111
500
x + 
4
125
y + 
629
125
z = 
103
100
    (1)
 
19
740
y + 
107
20
z = 
637
740
    (2)
 
7289
703
z = 
467
57
    (3)

Multiply both sides of equation (3) by 75221
Divide both sides of equation (3) by 145780, get the equation：
         
21079
3940
z = 
49969
11820
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
 
111
500
x + 
4
125
y + 
629
125
z = 
103
100
    (1)
 
19
740
y = - 
736193
218670
    (2)
 
7289
703
z = 
467
57
    (3)

Multiply both sides of equation (3) by 442187
Divide both sides of equation (3) by 911125, get the equation：
         
123913
24625
z = 
293743
73875
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 
111
500
x + 
4
125
y = - 
870607
295500
    (1)
 
19
740
y = - 
736193
218670
    (2)
 
7289
703
z = 
467
57
    (3)

Multiply both sides of equation (2) by 592
Divide both sides of equation (2) by 475, get the equation：
         
148
4625
y = - 
309976
73875
    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation：
 
111
500
x = 
123099
98500
    (1)
 
19
740
y = - 
736193
218670
    (2)
 z = 
467
591
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
1109
197
    (1)
 y = - 
77494
591
    (2)
 z = 
467
591
    (3)


Therefore, the solution of the equation set is:
x = 
1109
197
y = - 
77494
591
z = 
467
591


Convert the solution of the equation set to decimals:
x = 5.629442
y = -131.123519
z = 0.790186

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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