Question

what is the value of k for which the simultaneous equation 2x+3y=8 and 6x-ky=24 infinitely many solutions???​

Answer 1

Correct option is

A

4

4x+y=7 and 16x+ky=28

Comparing the above equation with the equation a

1

x+b

1

y=c

1

and

a

2

x+b

2

y=c

2

respectively.

a

1

=4,b

1

=1,c

1

=7,

a

2

=16,b

2

=k,c

2

=28

a

2

a

1

=

16

4

=

4

1

,

b

2

b

1

=

k

1

and

c

2

c

1

=

4

1

∴ The condition for the simultaneous equations to have infinitely many solutions is.

a

2

a

1

=

b

2

b

1

=

c

2

c

1

∴

4

1

=

k

1

=

4

1

∴

4

1

=

k

1

∴k=4.

Hence the simultaneous equations 4x+y=7 and 16x+ky=28 will have infinitely many solutions for k=4.

Answer 2

Answer:

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