Question

Write the condition of consistency of linear equations as+by+c, = 0 and ax+by+c=0 unique solution

Answer 1

Answer:

am



=bl

The given equations are ax+by=c

or ax+by−c=0 and

lx+my=n

or lx+my−n=0.

The equations have a unique solution.

So,

a

2

a

1



=

b

2

b

1

Here a

1

=a,a

2

=l,b

1

=b,b

2

=m,c

1

=−c,c

2

=−n

∴

a

2

a

1

=

l

a

,

b

2

b

1

=

m

b

.

∴

l

a



=

m

b

⇒am



=bl.

This is the required condition.