`10x + 14 y + 4 = 0``-10x - 14y +4 =0``-10 +14y +4 =0``10x - 14y + 4 = 0`
Answer : D
Solution : Condition for dependent linear equations
`[a_[1]]/[a_[2]] = [b_[1]]/[b_[2]] = c_[1]/[c_[2]] = [1]/[k]`
Give equation of line is, `-5x + 7y - 2 = 0`
Here, `" " a_[1] = -5, b_[1] = 7, c_[1] = -2`
From Eq. [i], `" " -[5]/[a_[2]] = [7]/[b_[2]] = - [2]/[c_[2]] = [1]/[k] " " ` [say]
`rArr " " a_[2] = -5k, b_[2] = 7k, c_[2] = -2k`
where, k is any arbitrary constant.
Putting k = 2, then `" " a_[2] = -10 , b_[2] = 14`
and `" " c_[2] = -4`
`:.` The required equation of line becomes
`" " a_[2] x + b_[2] y + c_[2] = 0`
`rArr " " -10x + 14y - 4 = 0`
`rArr " " 10x - 14y + 4 = 0`
Question 19 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ] - Solutions of Sample Papers for Class 10 Boards
Last updated at Sept. 6, 2021 by
One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation can be
[a] 10x + 14y + 4 = 0 [b] –10x – 14y + 4 = 0
[c] –10x + 14y + 4 = 0 [d] 10x – 14y = –4
This question is inspired from Question 11 - MCQs from NCERT Exemplar - Chapter 3 Class 10 - Pair of Linear Equations in Two Variables
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Question 19 One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation can be [a] 10x + 14y + 4 = 0 [b] –10x – 14y + 4 = 0 [c] –10x + 14y + 4 = 0 [d] 10x – 14y = –4 Given equation −5x + 7y − 2 = 0 Therefore, a1 = −5, b1 = 7 , c1 = –2 Since we want a dependent line, it means the lines are coincident For Coincident lines 𝒂𝟏/𝒂𝟐 = 𝒃𝟏/𝒃𝟐 = 𝒄𝟏/𝒄𝟐 Since, a1 = −5 , b1 = 7 , c1 = −2 a2, b2, c2 can be a2 = −10 , b2 = 14 , c2 = −4 Thus, a coincident line is −10x + 14y − 4 = 0 10x − 14y = −4 So, the correct answer is [D]
D. 10x - 14y + 4 = 0
Condition for dependent linear equations -
a1 /a2 = b1/b2 = c1/c2 …[i]
Given equation of line is, - 5x + 7y - 2 = 0;
Comparing with ax+ by +c = 0;
Here, a1 = - 5, b1 = 7, c1 = - 2;
For second equation, let’s assume a2x + b2y + c2 = 0;
From Eq. [i], -5/a2 = 7/b2 = -2/c2 = 1/k
Where, k is any arbitrary constant.
Putting k = - 1/2 then
a2 = 10, b2 = - 14, c2 = 4;
∴ The required equation of line becomes
a2x + b2y + c2 = 0;
10x - 14y + 4 = 0;
asked Sep 6, 2021 in Mathematics by
[35.3k points]
closed Sep 7, 2021 by Adarsh01
One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation can be
[a] 10x+14y +4 = 0
[b] –10x –14y+ 4 = 0
[c] –10x+14y + 4 = 0
[d] 10x – 14y = –4
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