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:
 2x 
3
4
y 
1
2
z = 11    (1)
3
4
x 
7
4
y = 4    (2)
3
4
x + z = -7    (3)
Question solving process:

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 8, the equation can be obtained:
         
3
4
x 
9
32
y 
3
16
z = 
33
8
    (4)
, then add the two sides of equation (4) to both sides of equation (2), the equations are reduced to:
 2x 
3
4
y 
1
2
z = 11    (1)
65
32
y 
3
16
z = 
65
8
    (2)
3
4
x + z = -7    (3)

Multiply both sides of equation (1) by 3
Divide the two sides of equation (1) by 8, the equation can be obtained:
         
3
4
x 
9
32
y 
3
16
z = 
33
8
    (5)
, then add the two sides of equation (5) to both sides of equation (3), the equations are reduced to:
 2x 
3
4
y 
1
2
z = 11    (1)
65
32
y 
3
16
z = 
65
8
    (2)
9
32
y + 
13
16
z = 
23
8
    (3)

Multiply both sides of equation (2) by 9
Divide the two sides of equation (2) by 65, the equation can be obtained:
        
9
32
y 
27
1040
z = 
9
8
    (6)
, then subtract both sides of equation (6) from both sides of equation (3), the equations are reduced to:
 2x 
3
4
y 
1
2
z = 11    (1)
65
32
y 
3
16
z = 
65
8
    (2)
 
109
130
z = -4    (3)

Multiply both sides of equation (3) by 195
Divide both sides of equation (3) by 872, get the equation:
         
327
1744
z = 
195
218
    (7)
, then add the two sides of equation (7) to both sides of equation (2), get the equation:
 2x 
3
4
y 
1
2
z = 11    (1)
65
32
y = 
6305
872
    (2)
 
109
130
z = -4    (3)

Multiply both sides of equation (3) by 65
Divide both sides of equation (3) by 109, get the equation:
         
109
218
z = 
260
109
    (8)
, then add the two sides of equation (8) to both sides of equation (1), get the equation:
 2x 
3
4
y = 
939
109
    (1)
65
32
y = 
6305
872
    (2)
 
109
130
z = -4    (3)

Multiply both sides of equation (2) by 24
Divide both sides of equation (2) by 65, get the equation:
        
3
4
y = 
291
109
    (9)
, then subtract both sides of equation (9) from both sides of equation (1), get the equation:
 2x = 
648
109
    (1)
65
32
y = 
6305
872
    (2)
 z = 
520
109
    (3)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
 x = 
324
109
    (1)
 y = 
388
109
    (2)
 z = 
520
109
    (3)


Therefore, the solution of the equation set is:
x = 
324
109
y = 
388
109
z = 
520
109


Convert the solution of the equation set to decimals:
x = 2.972477
y = -3.559633
z = -4.770642

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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