Expert: Richard J. Raridon - 10/19/2007

Question
Find k if the following system of equations has a unique solution.
2x + (k-1)y=6
3x+(2k+1)y=9

I came up with...a.2x+y*k-y-6=0   b.3x+y*2k+y-9=0
Are my answers correct?

Answer
no, all you did was multiply out the equations.
If you eliminate x from the equations you also eliminate y and end up with k = -5 which is the value for the two lines being parallel.  therefore, any value of k other than -5 will give you a unique solution.