The following pair of linear equations contains a parameter k:
kx+y=2k(k−1)x+(k+1)y=3k+1
Work through every part carefully.
a. (i) Determine the value(s) of k for which the pair of equations has no solution. Show complete working.
b. (ii) Find the value(s) of k for which the pair of equations has infinitely many solutions. Explain clearly why your result satisfies this condition.
c. (iii) For k=3, solve the pair of equations and then sketch both lines on the same Cartesian plane, clearly indicating their point of intersection and intercepts on the axes.