Question

For what value of p, will the following system of linear equations represent parallel lines? -x+py=1 and px-y=1
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

SOLUTION:

Given pair of equation is

-x+py=1………….(1)

px-y=1……………(2)

On comparing the given Equations with standard form
a1x+b1y+c1=0 and a2x+b2y+c2=0

a1= -1, b1= p, c1=-1
a2=p, b2=-1, c2=-1

A pair of linear equations will represent parallel lines i.e have no solution ,if

a1/a2 = b1/b2 ≠ c1/c2

-1/p = p/-1 ≠ -1/-1……………..(3)

I          II         III

On taking I and II terms we get

-1/p = p/-1

p²=1

p= ±1

Since , p=-1  does not satisfy the last two terms of equation (3)

Therefore p= 1 is the required value.

Hence, for p= 1, the given system of equation will represent parallel lines

HOPE THIS WILL HELP YOU....

Answer 2

-x+py=1
px-y=1

a1=-1. b1=p. c1=1
a2=p. b2=-1. c2=1

if equation represent parallel line,
a1/a2=b1/b2≠c1/c2

a1/a2=b1/b2
-1/p=p/-1
p²=1
p=±1


b1/b2≠c1/c2
p/-1≠1/1
p≠-1

so,the value of p will be 1 for the equation represent parallel line.