Question

For which value(s) of ݌ ,will the lines represented by the following pair of linear

equations be parallel

3x-y-5=0
6x-2y-p=0

a) all real values except 10

b) 10

c) 5/2

d) 1/2​

Answer 1

Answer: (a) all real values except 10

Given pair of linear equations is

3x - y - 5 = 0 …(i)

and 6x - 2y - p = 0 …(ii)

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

Here, a1 =3, b1 = - 1, c1 = - 5;

And a2 = 6, b2 = - 2, c2 = - p;

a1 /a2 =3/6 = 1/2

b1 /b2 = -1/-2 =1/2

c1 /c2 = 5/p

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

a1/a2 = b1/b2 not equal to c1/c2

Taking last two parts, we get;

1/2 not equal to 5/p

p is not equal to 10

So, p is not equal to 10

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

Answer 2

Answer:

(a) all real values except 10

Step-by-step explanation:

Given pair of linear equations is

3x - y - 5 = 0 …(i)

and 6x - 2y - p = 0 …(ii)

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

Here, a1 =3, b1 = - 1, c1 = - 5;

And a2 = 6, b2 = - 2, c2 = - p;

a1 /a2 =3/6 = 1/2

b1 /b2 = -1/-2 =1/2

c1 /c2 = 5/p

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

a1/a2 = b1/b2 not equal to c1/c2

Taking last two parts, we get;

1/2 not equal to 5/p

p is not equal to 10

So, p is not equal to 10

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