- #1

thatguythere

- 91

- 0

## Homework Statement

For what value(s) of

*k*

*does the system of linear equations below have a unique solution?*

2x+(

3x+(2

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

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.2x+(

*k*-1)y = 63x+(2

*k*+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.