Question 997848
.
a) Let k represent a Real Number.
y = 2x + k
y = 2x – k
------------------------------------------------------------


These equations represent parallel straight lines. 

These lines coincide if  k=0.  At this value of  k  the system has infinitely many solutions.


If  k=/=0,  then these lines are parallel and do not coincide.  The system has no solutions in this case. 



b) Let a represent a Real Number.
y = -2x + a
y = 12 x – a.


These straight lines have different slopes.  They are not parallel,  hence,  they have an intersection.  It means that the system has an unique solution.