Question

Given is the inconsistent system of linear equations, 2x + 7y = 11 and 5x + ky - 25 = 0, then k is ​

Answer 1

Answer:

The equations are 2x+ky=11 and 5x−7y=5

or 2x+ky−11=0 and 5x−7y−5=0

They will have no solution if

a

2

a

1

=

b

2

b

1



=

c

2

c

1

Here a

1

=2,a

2

=5,b

1

=k,b

2

=−7,c

1

=−11,c

2

=−5

∴

a

2

a

1

=

5

2

,

b

2

b

1

=

−7

k

,

c

2

c

1

=

−5

−11

=

5

11

Now from (1)

a

2

a

1

=

b

2

b

1

∴

5

2

=

−7

k

⇒k=

5

−14

Also the first two ratios



=

c

2

c

1

∴k=

5

−14

Hence, the value of k is

5

−14

Answer 2

Answer:

Refer The Attachment ...

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