Question

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

Answer 1

Step-by-step explanation:

your answer is 10 .............

Answer 2

For all real values of p except 10 the lines represented by the following pair of linear equations are parallel

Solution:

Need to find the value of p for which following pair of linear equation be parallel.

3x − y − 5 = 0

6x − 2y − p = 0

General form of pair of linear equation is  

$\begin{array}{l}{\mathrm{a}_{1} \mathrm{x}+\mathrm{b}_{1} \mathrm{y}+\mathrm{c}_{1}=0} \\ {\mathrm{a}_{2} \mathrm{x}+\mathrm{b}_{2} \mathrm{y}+\mathrm{c}_{2}=0}\end{array}$

For above general equation to be parallel, $\mathrm{a}_{1} / \mathrm{a}_{2}=\mathrm{b}_{1} / \mathrm{b}_{2} \text { not equal to } \mathrm{c}_{1} / \mathrm{c}_{2}$

$\text { In our case } a_{1}=3, b_{1}=-1, c_{1}=-5 \text { and } a_{2}=6, b_{2}=-2, c_{2}=-p$

So for given equations to be parallel

3/6 = (-1)/(-2 ) not equal to (-5)/(-p)

=> 1/2 not be equal to 5/p

=> p not equal to 10

Hence p can have any real value other than so that given linear pair of equations is parallel.

Hence correct option is (a) that is all real values except 10.