Question

The value of 'k',for which the system of equations x+(k+1)y=5 and (k+1)x+9y=8k-1 has infinite many solutions is​

Answer 1

Answer:

This system of equation is of the form

a

1

x+b

1

y=c

1

a

2

x+b

2

y=c

2

where a

1

=1,b

1

=k+1,c

1

=5

and a

2

=k+1,b

2

=9 and c

2

=8k−1

For infinitely many solutions, we must have

a

2

a

1

=

b

2

b

1

=

c

2

c

1

The given system of equations will have infinite solutions, if

k+1

1

=

9

k+1

=

8k−1

5

⇒

k+1

1

=

9

k+1

and

9

k+1

=

8k−1

5

⇒