Consider the equation 5x−7y=14. A second line is given by (5k)x−(7k)y=14k+3, where k is a real parameter.
a. (i) Without plotting, show that for k=1 the two equations represent parallel lines.
b. (ii) Find the value of k for which the two lines are coincident.
c. (iii) State the value(s) of k for which the pair of equations has a unique solution, and justify your answer.
d. (iv) For k=−2, solve the pair of equations and describe the nature of the solution set.