find the value of k for which the system of equations has a unique solution 2x+ky-9=0 , kx+3y-13=0.

Guest Jun 15, 2022

#1**+1 **

The system is equivalent to \(\begin{cases} 2x + ky &=& 9\\ kx + 3y &=& 13 \end{cases}\).

As long as the lines represented by the equations are not parallel, the system would have a unique solution.

\(-\dfrac2k \neq -\dfrac k3\\ k^2 \neq 6\\ k \neq \pm \sqrt 6\)

For \(k \neq \sqrt 6\) and \(k \neq -\sqrt 6\), the system has a unique solution.

MaxWong Jun 16, 2022