Chapter 9 - 9.2 - Two-Variable Linear Systems - 9.2 Exercises - Page 649: 61

$k=-4$

We have the two system of equations as follows: $4x-8y=-3 \\ 2x+ky =16$ The system is inconsistent when it has no solution. Thus, $\dfrac{4}{2}=\dfrac{-8}{k} \ne \dfrac{-3}{16}$ Now, $\dfrac{4}{2}=\dfrac{-8}{k} $ This implies that $k=-4$