For which value(s) of p, the lines represented by the pair of linear equations

3x − y − 5 = 0, 6x − 2y − p = 0 will be parallel?

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all real values except 10.

answer is D.

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Detailed Solution

The general form for a pair of linear equations in two variables x and y is

a 1 x + b 1 y + c 1 = 0 a 2 x + b 2 y + c 2 = 0.

Where

a 1, a 2, b 1, b 2, c 1, c 2

are all real numbers.
If

a 1 a 2 ≠ b 1 b 2

then the pair of linear equations has a unique solution and their graph represents intersecting lines.
If

a 1 a 2 = b 1 b 2 = c 1 c 2

then the pair of linear equations has a infinite solutions and their graph represents coincident lines.
If

a 1 a 2 = b 1 b 2 ≠ c 1 c 2

then the pair of linear equations has no solution and their graph represents parallel lines.
The given pair of linear equations are
3x − y − 5 = 0 ………(1)
6x − 2y − p = 0 ………(2)
We need to find the value(s) of ‘p’ for which the given pair of linear equations represent parallel lines.
Let us compare the given linear equation with the general form of pair of linear equations