Find the value(s) of the constant k such that the system of linear equations:

Question

9x+ky=3

kx+y=1

Answer 1

To have a unique solution, it is necessary and sufficient that the principal determinant of the system not be zero.  The principal determinant of this system is

 

D = 9(1) - k² ≠ 0

 

k² ≠ 9

 

k ≠ ±3

Answer 2

If k = 3 (write out the equations!) the two equations are consistent and dependent (all solutions the same).