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**3 x – y – 5 = 0 and 6x – 2y – p = 0, if the lines represented by these equations are parallel. Find p.**

Answer:

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

We get,

a_{1} = 3, b_{1} = – 1, c_{1} = – 5;

a_{2} = 6, b_{2} = – 2, c_{2} = – p;

a_{1} /a_{2} = 3/6 = ½

b_{1} /b_{2} = ½

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 ½ ≠ 5/p

So, p ≠ 10

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

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