Mathematics
语言：中文
Language:English

current location：Equations > Multivariate equations > Answer
Detailed information：
The input equation set is:
 20x -10y + 8z = 40    (1)
-10x + 24y + 4z = 20    (2)
 8x + 4y + 12z = 20    (3)
Question solving process:

Divide the two sides of equation (1) by 2, the equation can be obtained:
         10x -5y + 4z = 20    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
 20x -10y + 8z = 40    (1)
 19y + 8z = 40    (2)
 8x + 4y + 12z = 20    (3)

Multiply both sides of equation (1) by 2
Divide the two sides of equation (1) by 5, the equation can be obtained:
         8x -4y + 
16
5
z = 16    (5)
, then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
 20x -10y + 8z = 40    (1)
 19y + 8z = 40    (2)
 8y + 
44
5
z = 4    (3)

Multiply both sides of equation (2) by 8
Divide the two sides of equation (2) by 19, the equation can be obtained:
         8y + 
64
19
z = 
320
19
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 20x -10y + 8z = 40    (1)
 19y + 8z = 40    (2)
 
516
95
z = - 
244
19
    (3)

Multiply both sides of equation (3) by 190
Divide both sides of equation (3) by 129, get the equation：
         8z = - 
2440
129
    (7)
, then subtract both sides of equation (7) from both sides of equation (2), get the equation：
 20x -10y + 8z = 40    (1)
 19y = 
7600
129
    (2)
 
516
95
z = - 
244
19
    (3)

Multiply both sides of equation (3) by 190
Divide both sides of equation (3) by 129, get the equation：
         8z = - 
2440
129
    (8)
, then subtract both sides of equation (8) from both sides of equation (1), get the equation：
 20x -10y = 
7600
129
    (1)
 19y = 
7600
129
    (2)
 
516
95
z = - 
244
19
    (3)

Multiply both sides of equation (2) by 10
Divide both sides of equation (2) by 19, get the equation：
         10y = 
4000
129
    (9)
, then add the two sides of equation (9) to both sides of equation (1), get the equation：
 20x = 
11600
129
    (1)
 19y = 
7600
129
    (2)
 z = - 
305
129
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 x = 
580
129
    (1)
 y = 
400
129
    (2)
 z = - 
305
129
    (3)


Therefore, the solution of the equation set is:
x = 
580
129
y = 
400
129
z = - 
305
129


Convert the solution of the equation set to decimals:
x = 4.496124
y = 3.100775
z = -2.364341

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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