Let $n$ be the number obtained on rolling a fair die. If the probability that the system $x−ny+z=6$ $x+(n−2)y+(n+1)z=8$ $(n−1)y+z=1$ Has a unique solution is $\frac{k}{6},$ then the sum of $k$ and all possible values of $n$ is:

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Let \(n\) be the number obtained on rolling a fair die. If the probability that the system \(x−ny+z=6\) \(x+(n−2)y+(n+1)…

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