# Thread: Linear Algebra Systems?

1. ## Linear Algebra Systems?

If the following system has infinitely many solutions,
$\displaystyle -4x-5y-6z=6$
$\displaystyle -5x+7y+3z=7$
$\displaystyle 14x-9y+hz=k$
then k=?, h=?

I've been working on this and can't figure it out, could someone solve it and show me the answer as well as how they got to the answer? Thanks!

2. Originally Posted by ChingKing08
If the following system has infinitely many solutions,
$\displaystyle -4x-5y-6z=6$
$\displaystyle -5x+7y+3z=7$
$\displaystyle 14x-9y+hz=k$
then k=?, h=?

I've been working on this and can't figure it out, could someone solve it and show me the answer as well as how they got to the answer? Thanks!
do the gaussian elimination to get the row echelon form. it should have zero row in order to :
1. has no solution
2. has infinitely many solution

3. Originally Posted by dedust
do the gaussian elimination to get the row echelon form. it should have zero row in order to :
1. has no solution
2. has infinitely many solution
I've been trying that I just can't get the rows to work out right for some reason...I'll keep trying though. Thanks for helping me be certain I'm on the right track though, much appreciated.