Last updated at April 16, 2024 by Teachoo
Question 8 For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines? (A) 1/2 (B) − 1/2 (C) 2 (D) −2 3x − y + 8 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 3 , b1 = −1 , c1 = 8 6x − ky + 16 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 6 , b2 = −k, c2 = 16 Therefore, a1 = 3 , b1 = −1 , c1 = 8 & a2 = 6 , b2 = −k, c2 = 16 𝑎1/𝑎2 = 3/6 𝑎1/𝑎2 = 1/2 𝑏1/𝑏2 = (−1)/(−𝑘) 𝑏1/𝑏2 = 1/𝑘 𝑐1/𝑐2 = 8/16 𝑐1/𝑐2 = 2/2 Since the lines are coincident 𝒂𝟏/𝒂𝟐 = 𝒃𝟏/𝒃𝟐 = 𝒄𝟏/𝒄𝟐 1/2=1/𝑘=1/2 Thus, 1/2=1/𝑘 k = 2 So, the correct answer is (C)
