Question

The value of k, for which the system of equations x + (k + l)y = 5 and (k + l)x + 9y = 8k – 1

has infinitely many solutions is

(a) 2

(b) 3

(c) 4

(d) 5​

Answer 1

Answer:

2 has infinitely many solutions.........

Step-by-step explanation:

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Answer 2

Answer:

(a)2

Step-by-step explanation:

QUESTION: The Value of k, for which the system of equations x + (k + l)y = 5 and (k + l)x + 9y = 8k – 1.

To Find : The value of k.

Given: The system of equations has infinitely many solutions.

Concept: For a pair of linear equations to have infinitely many solutions,

a1/a2 = b1/b2 = c1/c2.

Explanation:-

x + (k+1)y = 5 ..(i)

(k+1)x + 9y = 8k-1 ..(ii)

Comparing with general form a1x+b1y = c1 and a2a + b2y = c2

We get a1 = 1, b1 = k+1, c1 = 5

a2 = k+1, b2 = 9, c2 = 8k-1

For a pair of linear equations to have infinitely many solutions,

a1/a2 = b1/b2 = c1/c2

=> 1/(k+1) = (k+1)/9 = 5/(8k-1) ..(i)

Take first and second in (i)

1/(k+1) = (k+1)/9

=> (k+1)2 = 9

=> k+1 = 3 or k+1 = -3

=> k = 2 or k = -4

Take first and last in (i)

1/(k+1) = 5/(8k-1)

=> 5(k+1) = 8k-1

=>> 5k+5 = 8k-1

=> 3k = 6

=> k = 2

Take second and third in (i)

(k+1)/9 = 5/(8k-1)

=> (k+1) (8k-1) = 45

=> 8k2+8k-k-1 = 45

=> 8k2+7k-46 = 0

=> k = 2 or k = -23/8

So k = 2 is the required value.

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