Question

Find the value of k for which the following pair of linear equations has coincident lines on the graphical
representation
kx + 4y =k+8
4x + ky+4=0​

Answer 1

Answer:

Given lines

kx + 4y + (4+8) = 0

4x + ky + 4= 0

for lines to have infinite solutions

a

2

a

1

=

b

2

b

1

=

c

2

c

1

[a

1

x+b

1

y+c

1

=0,a

2

x+b

2

y+c

2

=0]

∴

4

k

=

k

4

=

4

μ+8

∴

4

k

=

k

4

⇒k

2

=16 k=4

k

4

=

4

μ+8

k=±4

4

4

=

4

μ+8

k=−4⇒

−4

4

=

4

μ+8

μ=−4

=μ=−12

∴ for k=±4 The line has infinite solutions