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# System

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

Jun 15, 2022

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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.

Jun 16, 2022