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
Get live Maths 1-on-1 Classs - Class 6 to 12
CBSE Class 10 Sample Paper for 2019 Boards
Question 1
Question 2 (Or 1st)
Question 2 (Or 2nd) Important
Question 3 (Or 1st) Important
Question 3 (Or 2nd)
Question 4
Question 5 Important
Question 6 Important
Question 7 (Or 1st)
Question 7 (Or 2nd) Important
Question 8 (Or 1st)
Question 8 (Or 2nd)
Question 9
Question 10 Important
Question 11 Important
Question 12 Important You are here
Question 13 Important
Question 14
Question 15
Question 16 (Or 1st) Important
Question 16 (Or 2nd)
Question 17 (Or 1st) Important
Question 17 (Or 2nd)
Question 18 Important
Question 19 (Or 1st)
Question 19 (Or 2nd) Important
Question 20
Question 21 (Or 1st) Important
Question 21 (Or 2nd)
Question 22
Question 23 (Or 1st) Important
Question 23 (Or 2nd)
Question 24
Question 25
Question 26
Question 27 (Or 1st)
Question 27 (Or 2nd) Important
Question 28 (Or 1st)
Question 28 (Or 2nd) Important
Question 29
Question 30 Important
CBSE Class 10 Sample Paper for 2019 Boards
Last updated at March 23, 2023 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
Get live Maths 1-on-1 Classs - Class 6 to 12
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