Question

For what value of k, the equations 3x - y=-8 and 6x - ky =-16 represent the
coincident lines ?​

Answer 1

Answer:

The given equations are 3x-y+8=0 and 6x-ky+16 = 0. We have to find the point at which both the equations represent coincident lines.

For the lines to be coincident,

\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}

a

2

a

1

=

b

2

b

1

=

c

2

c

1

\text { Here } a_{1}=3, a_{2}=6, b_{1}=-1, b_{2}=-k, c_{1}=8 \text { and } c_{2}=16 Here a

1

=3,a

2

=6,b

1

=−1,b

2

=−k,c

1

=8 and c

2

=16

Substituting the values, we get

\frac{3}{6}=\frac{-1}{-k}=\frac{8}{-16}

6

3

=

−k

−1

=

−16

8

Either \frac{3}{6}=\frac{-1}{-k}

6

3

=

−k

−1

or \frac{-1}{-k}=\frac{8}{16}

−k

−1

=

16

8

k = 2 or k = 2

Therefore for k = 2, both the equations represent coincident lines.