SOLUTION: 3x+2y+z=3 x-3y+z=4 -6-4y-2z=1 I started the problem but can't seem to advance 3x+2y+z=3 x-3y+z=4 2x+5y=-1

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Question 692420: 3x+2y+z=3
x-3y+z=4
-6-4y-2z=1
I started the problem but can't seem to advance
3x+2y+z=3
x-3y+z=4
2x+5y=-1
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
3x+2y+z=3
x-3y+z=4
-6-4y-2z=1
---------------
There's no x term in the 3rd eqn
---
If you meant:
3x+2y+z=3
x-3y+z=4
-6x-4y-2z=1
then eqn 3 is 2 times eqn 1, but the RH side is different --> inconsistent
No solution.
Eqn's 1 & 3 give parallel planes in 3-space, no intersection.
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
 3x + 2y +  z = 3
  x - 3y +  z = 4
-6x - 4y - 2z = 1

The idea is to get a system that looks like this:

 Ax + By + Cz = D
      Ey + Fz = G
           Hz = I

And it's OK if the + signs are minuses.

Get rid of the x by multiplying the 2nd eq by -3
and adding the first equation to it:

 3x + 2y +  z =   3
-3x + 9y - 3z = -12
-------------------
     11y - 2z =  -9

So the system is now:

 3x +  2y +  z =  3
      11y - 2z = -9
-6x -  4y - 2z =  1

Get rid of the -6x by multiplying the 1st eq by 2
and adding the third equation to it:

 6x +  4y +  2 =  6
-6x -  4y - 2z =  1
-------------------
            0z =  7

We can stop right here and say there is no solution,
because no value of z multiplied by zero can give 7.
So we write:

No solution, the equations are inconsistent.

Edwin
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