For each real value of the parameter k, consider the system of equations
(k−1)x+2y=3,
(2k+1)x+(k+4)y=5.
a. (i) Determine the values of k for which the system has
(a) a unique solution, and
(b) no solution.
b. (ii) For every value of k that gives a unique solution, find the corresponding solution (x,y).