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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:
 90x + 85y + 75z = 81    (1)
 75x + 90y + 34z = 53    (2)
 89x + 89y + 55z = 69    (3)
Question solving process:

Multiply both sides of equation (1) by 5
Divide the two sides of equation (1) by 6, the equation can be obtained:
         75x + 
425
6
y + 
125
2
z = 
135
2
    (4)
, then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
 90x + 85y + 75z = 81    (1)
 
115
6
y - 
57
2
z = - 
29
2
    (2)
 89x + 89y + 55z = 69    (3)

Multiply both sides of equation (1) by 89
Divide the two sides of equation (1) by 90, the equation can be obtained:
         89x + 
1513
18
y + 
445
6
z = 
801
10
    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 90x + 85y + 75z = 81    (1)
 
115
6
y - 
57
2
z = - 
29
2
    (2)
 
89
18
y - 
115
6
z = - 
111
10
    (3)

Multiply both sides of equation (2) by 89
Divide the two sides of equation (2) by 345, the equation can be obtained:
         
89
18
y - 
1691
230
z = - 
2581
690
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 90x + 85y + 75z = 81    (1)
 
115
6
y - 
57
2
z = - 
29
2
    (2)
- 
4076
345
z = - 
2539
345
    (3)

Multiply both sides of equation (3) by 19665
Divide both sides of equation (3) by 8152, get the equation：
        - 
58083
2038
z = - 
144723
8152
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
 90x + 85y + 75z = 81    (1)
 
115
6
y = 
26519
8152
    (2)
- 
4076
345
z = - 
2539
345
    (3)

Multiply both sides of equation (3) by 25875
Divide both sides of equation (3) by 4076, get the equation：
        - 
76425
1019
z = - 
190425
4076
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation：
 90x + 85y = 
139731
4076
    (1)
 
115
6
y = 
26519
8152
    (2)
- 
4076
345
z = - 
2539
345
    (3)

Multiply both sides of equation (2) by 102
Divide both sides of equation (2) by 23, get the equation：
         85y = 
58803
4076
    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation：
 90x = 
20232
1019
    (1)
 
115
6
y = 
26519
8152
    (2)
 z = 
2539
4076
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
1124
5095
    (1)
 y = 
3459
20380
    (2)
 z = 
2539
4076
    (3)


Therefore, the solution of the equation set is:
x = 
1124
5095
y = 
3459
20380
z = 
2539
4076


Convert the solution of the equation set to decimals:
x = 0.220608
y = 0.169725
z = 0.622915

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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