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Question 12 - CBSE Class 10 Sample Paper for 2019 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 16, 2024 by Teachoo

Question 12

For what value of p will the following pair of linear equations have infinitely many solutions

(p – 3)x + 3y = p

px + py = 12

Transcript

Question 12 For what value of p will the following pair of linear equations have infinitely many solutions (p – 3)x + 3y = p px + py = 12 Given equations (p – 3)x + 3y = p px + py = 12 (p – 3)x + 3y = p (p – 3)x + 3y – p = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = (p – 3) , b1 = 3 , c1 = –p px + py = 12 px + py – 12 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = p , b2 = p , c2 = –12 Given that Equation has infinite number of solutions ∴ 𝑎1/𝑎2 = 𝑏1/𝑏2 = 𝑐1/𝑐2 Putting in values ((𝑝 − 3))/𝑝 = 3/𝑝 = (−𝑝)/(−12) ((𝑝 − 3))/𝑝 = 3/𝑝 = 𝑝/12 1/2 marks Solving ((𝒑 − 𝟑))/𝒑 = 𝟑/𝒑 p(p – 3) = 3p p2 – 3p = 3p p2 – 3p – 3p = 0 p2 – 6p = 0 p(p – 6) = 0 So, p = 0, 6 1/2 marks Solving 𝟑/𝒑 = 𝒑/𝟏𝟐 3 × 12 = p2 36 = p2 p2 = 36 p = ± √36 p = ± 6 So, p = 6, –6 1/2 marks Since p = 6 satisfies both equations. Hence, p = 6 is the answer 1/2 marks
  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

    3. CBSE Class 10 Sample Paper for 2019 Boards

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CBSE Class 10 Sample Paper for 2018 Boards →
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Solutions of Sample Papers for Class 10 Boards

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo