Question

Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:

3x – y – 5 = 0 and 6x – 2y – p = 0,

if the lines represented by these equations are parallel.

Answer 1

Given pair of linear equations is

3x – y – 5 = 0  ......(i)

6x – 2y – p = 0   ......(ii)

On comparing with ax + by + c = 0, we get

a₁ = 3, b₁ = – 1, c₁ = – 5

a₂ = 6, b₂ = – 2, c₂ = – p

`a_1/a_2 = 3/6 = 1/2`

`b_1/b_2 = 1/2`

`c_1/c_2 = 5/p`

Since, the lines represented by these equations are parallel, then

`a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

Taking last two parts, we get `1/2 ≠ 5/p`

So, p ≠ 10

Hence, the given pair of linear equations are parallel for all real values of p except 10.