Consider the system of linear equations involving two parameters and : Answer the…

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider the system of linear equations involving two parameters

m

and

k

(m + 1)x + 3y = 4

2x + (m - 3)y = k

Answer the following questions. (i) For

m = 2

, determine the value of

k

that makes the system inconsistent. Give reasons for each step taken. (ii) For

m = 2

, find the value of

k

that makes the system dependent. Support your answer with appropriate calculations. (iii) Taking

k = 5

, find all real values of

m

for which the system has a unique solution, and then obtain that solution.