For a certain value of $k$, the system \begin{align*} x + y + 3z &= 10, \\ -4x + 3y + 5z &= 7, \\ kx + z &= 3 \end{align*}has no solutions. What is this value of $k$?
By Cramer's Rule,
|1 1 3|
|-4 3 5| = 0
|0 k 1|
Then 7 - 17k = 0, so k = 7/17. Hope this helps!
