SOLUTION: For what value(s) of k, if any, will the system have no solution, a unique solution, and infinitely many solutions? (Enter your answers as a comma-separated list. If an answer does

Answer. If k = -1 then the system has infinitely many solutions.

        For any other value of k the system has a unique solution.

Solution. 

If k=-1 then the system has the form

-x + 2y =  3,    (1)
2x - 4y = -6.    (2)

Notice that the row of coefficients of the second equation is proportional 
to the row of coefficients of the first equation (with the proportionality coefficient -2). 
The right side terms are proportional with the same coefficient -2. 
It means that the system (1), (2) has infinitely many solutions.

Geometrically, equations (1) and (2) represent the same straight line in the coordinate plane.

For any other value of k the rows of coefficients are not proportional.
So the system has a unique solution.