A system of equations has no solution if there is no pair of an x-value and a y-value that make both equations true. If you solve a system of equations and get to an absolute truth a statement not involving variables that is true, you have infinitely many solutions. A system of equations has infinitely many solutions if there are infinitely many values of x and y that make both equations true. The approach is to find the value of k which makes the two lines parallel.
Finding the point of intersection of a family of lines. If our two lines have the same slope and the same y-intercept, they are actually the same exact line. Systems have only infinite solutions, when the lines are coincident and the lines have the same y-intercept. It's a safety feature so you don't overheat the engine should the thermostat fail. We apply the same approach to both questions. A system has no solution if the equations are inconsistent, they are contradictory. In other words, systems have infinite solutions, when the two lines are the same line. Find k so that the system has no solution.