Vector equation with no solution There exists a real number $k$ such that the equation
$\begin{pmatrix} -1 \\ -2 \end{pmatrix} + t\begin{pmatrix} 3 \\ -2 \end{pmatrix} = \begin{pmatrix} 5 \\ 0 \end{pmatrix} + s\begin{pmatrix} -4 \\ k \end{pmatrix}$
does not have any solutions in $t$ and $s$. Find $k$.
I am confused as to how I will find k so this equation has NO solutions. Any help is appreciated. 
Thanks

In order for the system of equations to have no solutions, the constituent equations must be linearly dependent.  
This occurs when $3k=(-2)(-4)\implies k=\frac{8}{3}$.
$$\bbox[5px,border:2px solid #C0A000]{\text{The system has no solutions when}\,\, k=8/3}$$
