If the lines represented by the equations 3x y 5 and 6x 2y p are parallel then the value of p is

4

For which value[s] of p, will the lines represented by the following pair of linear equations be parallel

3x – y – 5 = 0

6x – 2y – p = 0

Two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 will be parallel if

Here, in given equations,

∴ p ≠ 10

Therefore, p can take any real value other than 10.

Hence, option a is the correct answer.

Given pair of linear equations is

3x – y – 5 = 0  ......[i]

6x – 2y – p = 0   ......[ii]

On comparing with ax + by + c = 0 we get

We get,

a1 = 3, b1 = – 1, c1 = – 5

a2 = 6, b2 = – 2, c2 = – p

`a_1/a_2 = 3/6 = 1/2`

`b_1/b_2 = 1/2`

`c_1/c_2 = 5/p`

Since, the lines represented by these equations are parallel, then

`a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

Taking last two parts, we get `1/2 ≠ 5/p`

So, p ≠ 10

Hence, the given pair of linear equations are parallel for all real values of p except 10.

Question 4 - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Nov. 1, 2019 by

For which value[s] of p, will the lines represented by the following pair of linear equations be parallel

  3x − y − 5 = 0

  6x −2y − p = 0

[a] all real values except 10  [b] 10  [c] 5/2  [d] 1/2

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Transcript

Question 4 For which value[s] of p, will the lines represented by the following pair of linear equations be parallel 3x − y − 5 = 0 6x − 2y − p = 0 [a] all real values except 10 [b] 10 [c] 5/2 [d] 1/2 Given lines 3x − y − 5 = 0 and 6x − 2y − p = 0 3x − y − 5 = 0 Comparing with a1x + b1y + c1 = 0 a1 = 3, b1 = –1, c1 = –5 6x − 2y − p = 0 Comparing with a2x + b2y + c2 = 0 a2 = 6, b2 = –2, c2 = –p Now, Since lines are parallel 𝑎_1/𝑎_2 = 𝑏_1/𝑏_2 ≠ 𝑐_1/𝑐_2 Comparing 𝑎_1/𝑎_2 = 𝑏_1/𝑏_2 ≠ 𝑐_1/𝑐_2 3/6=[−1]/[−2] ≠ [−5]/[−𝑝] 1/2=1/2 ≠ 5/𝑝 Therefore, 1/2 ≠ 5/𝑝 p ≠ 5 × 2 p ≠ 10 So, correct answer is [a] – all real values except 10

1. Class 10
2. Solutions of Sample Papers for Class 10 Boards

CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

Find the value[s] of p in the following pair of equations: 3x y 5 = 0 and 6x 2y p = 0, if the lines represented by these equations are parallel. Maths Q&A

Solution

Step 1: Compute the ratios of coefficients.

Given: pair of linear equations is

3x-y- 5=06x-2y-p=0

On comparing the given equations with ax+by+c=0 , we get

a1=3, b1=-1,c1=-5a2=6,b2=-2,c2=- p

a1a2=36b1b2=12c1c2 =5p

Step 2: Compute the required value.

Since the lines represented by these equations are parallel.

Then the condition is:

a1a2=b1b2≠c1 c2

On considering the last two parts, we get

12≠5p⇒p≠10.

Hence, the given pair of linear equations are parallel for all real values of p except 10.

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