Study the following pair of linear equations containing a parameter : Attempt all…

MATHEMATICS · Multi-part · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables

Problem

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. (i) Find all real values of

k

for which the pair of equations possesses exactly one solution. (ii) For each value of

k

obtained in part (i), determine the corresponding solution

(x, y)

. (iii) Identify any real value(s) of

k

(if they exist) for which the pair of equations becomes inconsistent and explain your reasoning.