Study the following pair of linear equations containing a parameter k:
2x+3y=7(k−4)x+(2k+1)y=5
Attempt all parts sequentially.
a. (i) Find all real values of k for which the pair of equations possesses exactly one solution.
b. (ii) For each value of k obtained in part (i), determine the corresponding solution (x,y).
c. (iii) Identify any real value(s) of k (if they exist) for which the pair of equations becomes inconsistent and explain your reasoning.