Question

$\huge\color{red}\boxed{\colorbox{black}{Question:}}$
On Comparing the ratios
$\frac{a1}{a2} , \frac{b1}{b2}$
and
$\frac{c1}{c2}$
find out whether the following pair of linear equations intersect at a point, are parallel or coincident:
(i) 2x + y + 3 = 0,
3x + 2y + 6 = 0

​

Answer 1

Step-by-step explanation:

The given linear equation are

⇒9x+3y+12=0....(1)

⇒a

1

=9,b

1

=3,c

1

=12

⇒18x+6y+24=0...(2)

⇒a

2

=18,b

2

=6,c

2

=24

⇒

a

2

a

1

=

18

9

=

2

1

⇒

b

2

b

1

=

6

3

=

2

1

⇒

c

2

c

1

=

24

12

=

2

1

comparing

a

2

a

1

,

b

2

b

1

,

c

2

c

1

We have

a

2

a

1

=

b

2

b

1

=

c

2

c

1

Hence, the lines represented by eq1 and eq2 are coincident