How to add horizontal line for subtraction in array

I already have this:

\documentclass{article}
\usepackage{amsmath}

\begin{document}    
$k:\left\{ \begin{array}{cccccc}x & = & -3+3\lambda & \Big| & 4 & \Big| \\ y & = & 4-4\lambda & \Big| & -3 & \Big| \end{array} \right. \Rightarrow \left\{ \begin{array}{cccccc}4x & = & -12+12\lambda \\ -3y & = & -12+12\lambda \end{array} \right.$
\end{document}

I kind of want to have this:

What is the best way to get the subtraction line?