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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 $k$?

 Aug 9, 2021
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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!

 Aug 9, 2021

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