Question

What is the value
p in which the
which the System of linear
equation -×+py=1 and px-y = 1 represent parallel
line ?​

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

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