Question

In the equation below, k>0, −(k+1)x+ky+5k=1 – 2ky ; when expressed in the form ax+by+c=0 gives c=4.The values of ‘a’ and ‘b’ are

Answer 1

Answer:

Answer

We know that the system of equations

a

1

x+b

1

y=c

1

a

2

x+b

2

y=c

2

has no solution, if

a

2

a

1

=

b

2

b

1



=

c

2

c

1

Here, a

1

=3,b

1

=1,c

1

=1,a

2

=2k−1,b

2

=k−1,c

2

=2k+1

So, the given system of equations will have no solution, if

2k−1

3

=

k−1

1



=

2k+1

1

2k−1

3

=

k−1

1

and

k−1

1



=

2k+1

1

Now,

2k−1

3

=

k−1

1

⇒3k−3=2k−1⇒k=2

Clearly, for k=2 we have

k−1

1



=

2k+1

1

Hence, the given system of equations will have no solution, if k=2.