Question

Find the value of p, for the following pair of equation 3x-y-5=0 and 6x-2y-p=0 are parallel

Answer 1

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Answer 2

Answer:

The pair of linear equations 3x-y-5=0 and 6x-2y-p=0 are parallel for all the values of 'p' other than 10

Step-by-step explanation:

Given

3x-y-5=0 and 6x-2y-p=0 are parallel

To find,

The value of 'p'

Recall the concept

A pair of linear equations $a_1x+b_1y+c1 = 0$  $a_2x+b_2y+c_2 = 0$ are parallel if $\frac{a_1}{a_2} = \frac{b_1}{b_2}\neq \frac{c_1}{c_2}$ -------------------(1)

Solution

Given equations are

3x-y-5=0 and 6x-2y-p=0

Compare the given equations with  $a_1x+b_1y+c1 = 0$ and $a_2x+b_2y+c_2 = 0$  we get

$a_1$ = 3 ,$a_2$ = 6 , $b_1$ = -1, $b_2$ = -2 $c_1$ = -5 and $c_2$ = -p

Substituting these values in the condition(1) we get

$\frac{3}{6} = \frac{-1}{-2} \neq \frac{-5}{-p}$

$\frac{1}{2} \neq \frac{5}{p}$

p ≠10

The pair of linear equations 3x-y-5=0 and 6x-2y-p=0 are parallel for all the values of 'p' other than 10

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