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
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
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
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
CBSE Class 10 Sample Paper for 2019 Boards
About the Author