**
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

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Last updated at Oct. 1, 2019 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

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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

CBSE Class 10 Sample Paper for 2019 Boards

Paper Summary

Question 1

Question 2 (Or 1st)

Question 2 (Or 2nd)

Question 3 (Or 1st)

Question 3 (Or 2nd)

Question 4

Question 5

Question 6

Question 7 (Or 1st)

Question 7 (Or 2nd)

Question 8 (Or 1st)

Question 8 (Or 2nd)

Question 9

Question 10

Question 11

Question 12 You are here

Question 13

Question 14

Question 15

Question 16 (Or 1st)

Question 16 (Or 2nd)

Question 17 (Or 1st)

Question 17 (Or 2nd)

Question 18

Question 19 (Or 1st)

Question 19 (Or 2nd)

Question 20

Question 21 (Or 1st)

Question 21 (Or 2nd)

Question 22

Question 23 (Or 1st)

Question 23 (Or 2nd)

Question 24

Question 25

Question 26

Question 27 (Or 1st)

Question 27 (Or 2nd)

Question 28 (Or 1st)

Question 28 (Or 2nd)

Question 29

Question 30

Class 10

Solutions of Sample Papers for Class 10 Boards

- CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard
- CBSE Class 10 Sample Paper for 2021 Boards - Maths Basic
- CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard
- CBSE Class 10 Sample Paper for 2020 Boards - Maths Basic
- CBSE Class 10 Sample Paper for 2019 Boards
- CBSE Class 10 Sample Paper for 2018 Boards

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.