SOLUTION: 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

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?
---
Yes. Each equation is a plane. They may meet in a point, or in
a line or not at all:
------------------------
Mske the 3rd equation the 1st:
-3x-6y+2z=5
6x+2y+4z=2
3x+4y-8z=-3
------------------
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
----------------------
Make the 3rd equation the 2nd:
-3x-6y+2z=5
0x-2y-6z=2
0x-10y+8z=12
----------------------
Divide thru the 2nd by -2
Divide thru the 3rd by 2:
-3x-6y+2z=5
0x+y+3z=-1
0x-5y+4z=6
--------------------
Add 5 times the 2nd Eq. to the 3rd to get:
-3x-6y+2z=5
0x+y+3z=-1
0x+0y+19z=1
----------------------
z = 1/19
-------------------
Substitute into the 2nd equation and solve for "y":
y + 3(1/19) = (-19/19)
y = -22/19
-------------------
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
==========================-
Conclusion: The three planes meet in the
point (13/19, -22/19, 1/19)
=====================================
Cheers,
Stan H.

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