Solving for h & k: No Solution?

[KevinL]

Homework Statement

Determine all values of h and k for which the system has no solution:

5x + 3y + 6z = -5
-6x - 7y - 4z = 9
-17x - 17y + hz = k

k =! ?
h = ?

The Attempt at a Solution

I googled the question and apparently most people solve this with a matrix, but we haven't gotten far enough in the class where we manipulate matrices or anything of the sort. Nor have we done an example of this in class. I am a bit clueless as to both what the question is asking and of course how to go about solving it.

 

[cc10]

That's a system of equations with 3 variables. So, if you don't want to solve it using matrices, simply solve for x, y, and z in terms of k and h, like you would solve a normal system of equations. At that point it will be easy to determine which values of h and k give no solution to the system.