Question

find out the value of K,if the lines 3x+5y=7and 12x-Ky=5 are parallel.​

Answer 1

Step-by-step explanation:

The straight lines :

2x+ky=1

3x−5y=7

Comparing 2x+ky=1

with a

1

x+b

1

y+c

1

=0

a

1

=2,b

1

=k,c

1

=−1

Comparing 3x−5y=7

with a

2

x+b

2

y+c

2

=0

a

2

=3,b

2

=−5,c

2

=−7

∴ For a unique solution ,

a

2

a

1



=

b

2

b

1

⇒

3

2



=

−5

k

∴k



=

3

−10

For infinite solutions ,

a

2

a

1

=

b

2

b

1

=

c

2

c

1

⇒

3

2

=

−5

k

=

7

1

thereisnosuchvalueofkwhichwillsatisfytheequation

For no solutions :

a

2

a

1

=

b

2

b

1



=

c

2

c

1

⇒

3

2

=

−5

k

∴k=−

3

10