x - 2y + z = -2
x + y - 2z = 4
-2x + y + z = 12
Solve the simultaneous equation x - 2y + z = -2 x + y - 2z = 4 -2x + y + z = 12?
2018-01-03 10:19 pm
回答 (5)
2018-01-03 10:39 pm
x - 2y + z = -2 …… [1]
x + y - 2z = 4 …… [2]
-2x + y + z = 12 …… [3]
[1]*2 :
2x - 4y + 2z = -4 ….. [1']
[2]*2 :
2x + 2y - 4z = 8 …… [2']
[3] + [1'] :
(-2x + 2x) + (y - 4y) + (z + 2z) = 12 - 4
-3y + 3z = 8
3y - 3z = 8 …… [4]
[3] + [2'] :
(-2x + 2x) + (y + 2y) + (z - 4z) = 12 + 8
3y - 3z = 20 …… [5]
[4] and [5] are contradictory.
Hence, the equation system has no solution.
x + y - 2z = 4 …… [2]
-2x + y + z = 12 …… [3]
[1]*2 :
2x - 4y + 2z = -4 ….. [1']
[2]*2 :
2x + 2y - 4z = 8 …… [2']
[3] + [1'] :
(-2x + 2x) + (y - 4y) + (z + 2z) = 12 - 4
-3y + 3z = 8
3y - 3z = 8 …… [4]
[3] + [2'] :
(-2x + 2x) + (y + 2y) + (z - 4z) = 12 + 8
3y - 3z = 20 …… [5]
[4] and [5] are contradictory.
Hence, the equation system has no solution.
2018-01-04 12:18 am
x - 2y + z = -2
x + y - 2z = 4
-2x + y + z = 12
3y - 3z = 6
2x - 4y + 2z = -4
-3y + 3z = 8
No solutions exist.
x + y - 2z = 4
-2x + y + z = 12
3y - 3z = 6
2x - 4y + 2z = -4
-3y + 3z = 8
No solutions exist.
2018-01-03 10:35 pm
no solution
2018-01-03 10:33 pm
x -2y +z = -2 -------(1)
x +y -2z = 4 ----------(2)
-2x+ y + z = 12 ------(3)
multiply equation (2) by -1
-x -y + 2z = -4
x -2y + z = -2 -------(1)
add:
-3y+3z = -6 ----------(4)
multiply equation (2) by 2
2x +2y - 4z = 8
-2x+y + z = 12 --------(3)
add:
3y -3z = 20 -------(5)
Solve (4) & (5)
-3y+3z = -6 ----(4)
3y-3z = 0 ------(5)
add:
0y+0z = -6
This system has no solution
(Inconsistent)
x +y -2z = 4 ----------(2)
-2x+ y + z = 12 ------(3)
multiply equation (2) by -1
-x -y + 2z = -4
x -2y + z = -2 -------(1)
add:
-3y+3z = -6 ----------(4)
multiply equation (2) by 2
2x +2y - 4z = 8
-2x+y + z = 12 --------(3)
add:
3y -3z = 20 -------(5)
Solve (4) & (5)
-3y+3z = -6 ----(4)
3y-3z = 0 ------(5)
add:
0y+0z = -6
This system has no solution
(Inconsistent)
2018-01-03 10:20 pm
Solve for X, Y,and Z in the following systems of three equations:
a. X + 2Y + Z = 6
X + Y =4
3X + Y + Z = 8
b. 10X + Y + Z = 12
8X + 2Y +Z =11
20X - 10Y -2Z = 8
c. 22X + 5Y + 7Z = 12
10X + 3Y + 2Z =5
9X + 2Y + 12Z = 14
a. X + 2Y + Z = 6
X + Y =4
3X + Y + Z = 8
b. 10X + Y + Z = 12
8X + 2Y +Z =11
20X - 10Y -2Z = 8
c. 22X + 5Y + 7Z = 12
10X + 3Y + 2Z =5
9X + 2Y + 12Z = 14
收錄日期: 2021-04-18 18:02:28
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https://hk.answers.yahoo.com/question/index?qid=20180103141908AAJohcM