Question

Find the value of k for which the following
pair of linear equations have infinitely many
solutions.
2x + 3y = 7, (k + 1)x + (2k - 1)y = 4k + 1
(Delhi 2019)​

Answer 1

• k equal 5 is the answer for the question.

Answer 2

Step-by-step explanation:

Given , 2x-3y = 7 ______ (1)

(k+1) x + (1-2k) y = 5k - 4  ______ (2)

Here a1=2,b1=−3,c1=7

a2=k+1,b2=1−2k,c3=5k−4

Since equations (1) and (2) have infinite solutions

a2a1=b2b1=c3c1

⇒k+12=1−2k−3=5k−47

∴k+12=1−2k3

⇒2(1−2k)=−3(k+1)

⇒2−4k=−3k−3

⇒2+3=−3k+4k

⇒