Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

For what value of n, does the system of linear equations
$2 x + 3 y = 7, (n − 1) x + (n + 2) y = 3 n$ have an infinite number of solutions?

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

It is given that the pair of linear equations

2 x + 3 y = 7

and

(n − 1) x + (n + 2) y = 3 n

have infinite number of solutions. We need to find the value of k.
A system of linear equations

a 1 x + b 1 y + c 1 = 0

and

a 2 x + b 2 y + c 2 = 0

has infinite solutions when

a 1 a 2 = b 1 b 2 = c 1 c 2

.
From equations

2 x + 3 y = 7

and

(n − 1) x + (n + 2) y = 3 n

, we have,

a 1 = 2, b 1 = 3, c 1 = − 7

and

a 2 = (n − 1), b 2 = (n + 2), c 2 = − 3 n

Thus, putting the values in the condition we have,

2 n − 1 = 3 n + 2 = 7 3 n

On comparing we have,

2 n − 1 = 3 n + 2 ⇒ 2 (n + 2) = 3 (n − 1) ⇒ 2 n + 4 = 3 n − 3 ⇒ 3 n − 2 n = 4 + 3 ⇒ n = 7

Thus, the value of n is 7.
Therefore, option 4 is correct.

Watch 3-min video & get full concept clarity