Question

One equation of a pair of dependent linear equations is –5x + 7y – 2 = 0. 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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Answer 1

Answer: (D) 10x-14y=-4

Explanation: For dependent pair, the two lines must have

a1/A2=b1/b2=c1/c2

for option (D)

a1/A2=b1/b2=c1/c2= -1/2

hope it's helps you ❤️

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

One equation of a pair of dependent linear equations is –5x + 7y – 2 = 0. The second equation can be

(A) 10x + 14y + 4 = 0                                                

(B) –10x – 14y + 4 = 0

(C) –10x + 14y + 4 = 0                                  

(D) 10x – 14y = - 4

CONCEPT TO BE IMPLEMENTED

A pair of Straight Lines

$\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

Is said to be consistent if $\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2}= \frac{c_1}{c_2}$

EVALUATION

One One equation of a pair of dependent linear equations is –5x + 7y – 2 = 0

Therefore

$\displaystyle \: a_1 = - 5\: , \: b_1 = 7</p><p>4 \: , c_1= - 2\:$

Now $\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2}= \frac{c_1}{c_2}$ gives

$\displaystyle \: \: \frac{-5}{a_2} = \frac{7}{b_2}= \frac{-2}{c_2}$

So one of the set is

$\displaystyle \: \: a_2 = - 10\: , \: b_2 = 14\: , \: \: c_2= - 4$

So one of the line is - 10x +14y - 4= 0

Which can be rewritten as 10x – 14y = - 4

FINAL ANSWER

Hence the correct option is

                             

 (D) 10x – 14y = - 4

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