Question

The value of k for which the pair of linear equation 2x-3y=6 and 12x+ky-5=0 has no solution is ​

Answer 1

Step-by-step explanation:

The given pair of linear equation can be written as

kx+3y−k+3=0 and 12x+ky−k=0

Here, a

1

=k,b

1

=3,c

1

=−k+3 and a

2

=12,b

2

=k,c

2

=−k

Now, the given pair of linear equation has no solution if

a

2

a

1

=

b

2

b

1



=

c

2

c

1

⇒

12

k

=

k

3



=

−k

−k+3

12

k

=

k

3

and

k

3



=

k

k−3

k

2

=36 and 3



=k−3

k=±6 and k



=6

k=−6

Hence, the given pair of linear equation has no solution if k=−6.

Answer 2

Answer:

by elimanition method

Step-by-step explanation:

2x+3y=6 multiple by 6

12x +18y =36

subtraction in equation

12 x. +18y=36

12 x+ky=5

18k=31

k=31/18

now putting the value of the equation 2

12x+31/18y=5

by LCM

216x+31y/18=5

247xy/18=5

247xy=5×18

247xy=90

xy=247-90

xy=157