The system of inequalities depends on a real parameter and is given by (k-2)x + y 4

MATHEMATICS · Subjective · CBSE · Mathematics · Linear Inequalities · Linear Inequalities

Problem

The system of inequalities depends on a real parameter

k

and is given by

(k-2)x + y \le 4, \quad x - 3y > -9.

(a) For the fixed point

P(2,-1)

, determine all real values of

k

for which

P

satisfies both inequalities. (b) For the values of

k

obtained in part (a), test whether the origin

O(0,0)

is also a solution of the system. Give a full justification in each case. (c) Explain how the sign of

k-2

affects the comparison symbol when the first inequality is rearranged with

y

as the subject.