Question

6.The value of c for which the pair of equations cx - y=2 and 8x - 2y=3 will have infinitely many solutions, is

Answer 1

Answer:

When there are two consistent equations as

a

1

x+b

1

y+c

1

=0&a

2

x+b

2

y+c

2

=0 then the equations will have infintely many solutions when the lines are coincident

i.e

a

2

a

1

=

b

2

b

1

=

c

2

c

1

The equations are not coincident if

a

2

a

1

=

b

2

b

1



=

c

2

c

1

Here the equations are

cx+y=2 and 6x+2y=3

So, a

1

=c,b

1

=1,c

1

=−2 and a

2

=6,b

2

=2,c

2

=−3

∴

a

2

a

1

=

6

c

,

b

2

b

1

=

2

1

and

c

2

c

1

=

−3

−2

=

3

2

Here we see that,

b

2

b

1



=

c

2

c

1

.

The lines are not coincident.

i.e we cannot assign any value to c.

Answer 2

Answer:

Condition for infinitely many solutions

$\frac{a}{a'} = \frac{b}{b'} = \frac{c}{c'}$

The given lines are cx - y=2 and 8x - 2y=3

Here a=c,b= -1,c= -2 and a'=8 ,b'= -2,c'= -3

=$\frac{ c}{ 8} = \frac{ - 1}{ - 2} = \frac{ - 2}{ - 3}$

Here,$\frac{c}{8} = \frac{1}{2}$ and $\frac{c}{8} = \frac{2}{3}$

=>c =4 and c=5.3

Since ,c has different values.

Hence ,for no value of c the pair of equations will have infinitely many solutions.

Hope this answer helps you out.