# Misc 9 - Chapter 10 Class 11 Straight Lines (Term 1)

Last updated at Feb. 3, 2020 by

Last updated at Feb. 3, 2020 by

Transcript

Misc 9 Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point. Let lines be 3x + y – 2 = 0 px + 2y – 3 = 0 2x – y – 3 = 0 Three line may intersect at one point Finding point of intersection of line (1) & (3) From (1) 3x + y − 2 = 0 3x + y = 2 y = 2 – 3x Putting value of y in (3) 2x – y − 3 = 0 2x − (2 − 3x) − 3 = 0 2x − 2 + 3x − 3 = 0 5x − 5 = 0 5x = 5 x = 5/5 x = 1 Putting x = 1 in (1) 3x + y – 2 = 0 3(1) + y – 2 = 0 3 + y – 2 = 0 y = 2 − 3 y = −1 Hence point of intersection of line (1) & (3) is (1, −1) Given that line (1), (2) & (3) may intersect at one point Hence point (1, −1) will lie on the 2nd line px + 2y − 3 = 0 i.e. (1, −1) satisfy the equation of line Putting x = 1, & y = −1 in (2) px + 2y − 3 = 0 p(1) + 2( −1) − 3 = 0 p − 2 − 3 = 0 p − 5 = 0 p = 5 Hence, for p = 5 the given lines intersect at one point

Miscellaneous

Misc 1
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Misc 2 Important

Misc 3 Important

Misc 4

Misc 5

Misc 6 Important

Misc 7

Misc 8 Important

Misc 9 Important You are here

Misc 10

Misc 11 Important

Misc 12 Important

Misc 13

Misc 14

Misc 15 Important

Misc 16 Important

Misc 17

Misc 18 Important

Misc 19 Important

Misc 20 Important

Misc 21 Important

Misc 22 Important

Misc 23

Misc 24 Important

Chapter 10 Class 11 Straight Lines (Term 1)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.