Examples

Chapter 3 Class 10 Pair of Linear Equations in Two Variables
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### 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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.