Question

The value of c for which the pair of equations 6 –4y = cx and

6x –2y = -3 will have infinite many solutions is……….

(a) -9 (b) 12 (c) 9 (d) -1​

Answer 1

Answer:

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Step-by-step explanation:

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.