Question

find the value of k. for infinite many solution x+(k+1)y=7. and (k+1)x+16y=9k+1​

Answer 1

Answer:

Step-by-step explanation:

Consider the given equations.

2x+3y=7

(k−1)x+(k+2)y=3k

 

The general equations

a  

1

​  

x+b  

1

​  

y=c  

1

​  

 

a  

2

​  

x+b  

2

​  

y=c  

2

​  

 

 

So,

a  

1

​  

=2,b  

1

​  

=3,c  

1

​  

=7

a  

2

​  

=k−1,b  

2

​  

=k+2,c  

2

​  

=3k

 

We know that the condition of infinite solution

a  

2

​  

 

a  

1

​  

 

​  

=  

b  

2

​  

 

b  

1

​  

 

​  

=  

c  

2

​  

 

c  

1

​  

 

​  

 

 

Therefore,

k−1

2

​  

=  

k+2

3

​  

=  

3k

7

​  

 

⇒  

k−1

2

​  

=  

k+2

3

​  

 

⇒2k+4=3k−3

⇒k=7

 

Hence, the value of k is 7.