## Elementary Linear Algebra 7th Edition

We have to choose $k=-2$.
Step 1: Make the right sides of the equations equal. This can be done by multiplying the second equation by $-2$: \begin{align*} 4x+ky=&6\\ -2kx-2y=&6 \end{align*} Step 2: Now since we want infinitely many solutions we want that the left sides of the equations be identical (same coefficients multiplying $x$ and $y$) so that we really have only one independent equation. If we choose $k=-2$ this will be the case because then we will have: \begin{align*} 4x-2y=&6\\ 4x-2y=&6 \end{align*} which is what we wanted.