- #1
thatguythere
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Homework Statement
For what value(s) of k does the system of linear equations below have a unique solution?
2x+(k-1)y = 6
3x+(2k+1)y= 9
Homework Equations
The Attempt at a Solution
I'm uncertain how to even go about tackling this problem. Given how all the other problems beforehand were dealing with matrices, I suppose I should start there, however the variable k throws me for a loop.
2x+ky-y = 6
3x+2ky+y = 9
[2 y -1 6] 1/2R1
[3 2y 1 9]
[1 y/2 -1/2 3] -3R1+R2
[3 2y 1 9]
[1 y/2 -1/2 3] 2R2
[0 y/2 5/2 0]
[1 y/2 -1/2 3]
[0 y 5 0] 1/yR2
[1 y/2 -1/2 3]
[0 1 5/y 0]
That is as far as I get in my blind attempt before I get stuck and no longer have any idea what I am doing. :) Any help would be greatly appreciated.