Question

For what value of , the following pair of equations will have a unique solutions?

4 + 3 = 3 8 + = 5​

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

Step-by-step explanation:

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