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Question 239168: if i were to need to find the point that three lines share is it possible for there to be no solution?
the problem is
6x+2y+4z=2
3x+4y-8z=-3
-3x-6y+2z=5
Thank you
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! if i were to need to find the point that three lines share is it possible for there to be no solution?
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Yes. Each equation is a plane. They may meet in a point, or in
a line or not at all:
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Mske the 3rd equation the 1st:
-3x-6y+2z=5
6x+2y+4z=2
3x+4y-8z=-3
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Add twice the 1st equation to the 2nd
Add the 1st equation to the 3rd:
-3x-6y+2z=5
0x-10y+8z=12
0x-2y-6z=2
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Make the 3rd equation the 2nd:
-3x-6y+2z=5
0x-2y-6z=2
0x-10y+8z=12
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Divide thru the 2nd by -2
Divide thru the 3rd by 2:
-3x-6y+2z=5
0x+y+3z=-1
0x-5y+4z=6
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Add 5 times the 2nd Eq. to the 3rd to get:
-3x-6y+2z=5
0x+y+3z=-1
0x+0y+19z=1
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z = 1/19
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Substitute into the 2nd equation and solve for "y":
y + 3(1/19) = (-19/19)
y = -22/19
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Substitute into the 1st equation to solve for "x":
-3x-6y+2z=5
-3x -6(-22/19) +2(1/19) = 5
-3x + 132/19 + 2/19 = 95/19
-3x = -39/19
x = 13/19
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Conclusion: The three planes meet in the
point (13/19, -22/19, 1/19)
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Cheers,
Stan H.
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