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Q.

For what value of p, the following pair of linear equations represent parallel lines? $2 x + 3 y = 8 (p − 1) x + (p + 1) y = 3 p − 1$

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a

2

b

4

c

5

d

6

answer is C.

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Detailed Solution

Given pair of equations are,

2 x + 3 y = 8 (p − 1) x + (p + 1) y = 3 p − 1

Two lines

a x_{1} + {by}_{1} + c_{1} = 0

and

a x_{2} + {by}_{2} + c_{2} = 0

are parallel only if

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

.
Since, equations are parallel,

a 1 a 2 = b 1 b 2

According to the question,

a 1 = 2 a 2 = (p − 1) b 1 = 3 b 2 = (p + 1)

Therefore,

2 p − 1 = 3 p + 1 ⇒ 2 p + 2 = 3 p − 3 ⇒ p = 5

The value is

p = 5

.
Hence, option 3 is correct.

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For what value of p, the following pair of linear equations represent parallel lines? 2x+3y =8 (p−1)x+(p+1)y =3p−1