Question

find the value of k for which the system of equation has
Infinitly many solution 2x-3y=7 and (k+1)x+(1-2k)y=(5k-4)​

Answer 1

Answer:

Hence, the value of k is 5 for which given equations have infinitely many solutions.

Step-by-step explanation:

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

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

Here a

1

=2,b

1

=−3,c

1

=7

a

2

=k+1,b

2

=1−2k,c

3

=5k−4

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

a

2

a

1

=

b

2

b

1

=

c

3

c

1

⇒

k+1

2

=

1−2k

−3

=

5k−4

7

∴

k+1

2

=

1−2k

3

⇒2(1−2k)=−3(k+1)

⇒2−4k=−3k−3

⇒2+3=−3k+4k

⇒k=5