Question

for which value of p, will the lines represented by the following pair of linear equation be parallel 3x-y-5=0 , 6x-2y-p=0​

Answer 1

Step-by-step explanation:

3x-y-5=0

so 3x-y=5 (1st equation)

now multiply the equation by 2

(3x-y=5)×2

= 6x-2y=10

but as per the question

6x-2y-p=0

6x-2y=p

substitute the equations

p=10

Answer 2

Answer:  The given lines are parallel for all values of p.

Step-by-step explanation:  We are given to find the value of p for which the lines represented by the following pair of linear equations are parallel :

$3x-y-5=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\6x-2y-p=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

We know that two straight lines are parallel if and only if they have equal slopes.

The slope-intercept form of a straight line is

$y=mx+c,$ where m is the slope and c is the y-intercept of the line.

From equation (i), we have

$3x-y-5=0\\\\\Rightarrow y=3x-5.$

So, slope, m = 3.

From equation (ii), we have

$6x-2y-p=0\\\\\Rightarrow 2y=6x-p\\\\\Rightarrow y=3x-\dfrac{p}{2}.$

So, slope, m' = 3.

Since, for all values of p, the slopes of both the lines is 3, so the lines will be always parallel.

Thus, the given lines are parallel for all values of p.