MATHEMATICS · Multi-part · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables
Problem
Consider the equation 5x−7y=14. A second line is given by (5k)x−(7k)y=14k+3, where k is a real parameter.
(i) Without plotting, show that for k=1 the two equations represent parallel lines.
(ii) Find the value of k for which the two lines are coincident.
(iii) State the value(s) of k for which the pair of equations has a unique solution, and justify your answer.
(iv) For k=−2, solve the pair of equations and describe the nature of the solution set.