Check sibling questions

Example 16 - For what values of k will the pair of linear

Example 16 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2
Example 16 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 3

This video is only available for Teachoo black users

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Example 16 For what values of k will the following pair of linear equations have infinitely many solutions? kx + 3y – (k-3) = 0 12x + ky – k = 0 kx + 3y – (k – 3) = 0 12x + ky – k = 0 kx + 3y – (k – 3) = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = k , b1 = 3 , c1 = – (k – 3) 12x + ky – k = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 12 , b2 = k , c2 = –k Since equation has infinite number of solutions So, 𝑎1/𝑎2 = 𝑏1/𝑏2 = 𝑐1/𝑐2 Putting values 𝑘/12 = 3/𝑘 = (−(𝑘 − 3))/(−𝑘) 𝑘/12 = 3/𝑘 = (𝑘 − 3)/𝑘 Solving 𝒌/𝟏𝟐 = 𝟑/𝒌 k2 =12 × 3 k2 = 36 k = ±√36 k = ± √62 k = ± 6 So, k = 6, – 6 Solving 𝟑/𝒌 = (𝒌 −𝟑)/𝒌 3k = k(k -3) 3k = k2 – 3k 0 = k2 – 3k – 3k k2 – 3k – 3k = 0 k2 – 6k = 0 k(k – 6) = 0 So, k = 0 , k = 6 Since k = 6 satisfies both equations. Hence, k = 6 is the answer

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.