by comparing the ratios a1/a2,b1/b2,c1/c2,state whether the line represented by the following pairs of linear equation intersect at a point are parallel or are coincident 9x+3y+12=0 18x+6y+24=0
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On comparing the ratios
a
2
a
1
,
b
2
b
1
and
c
2
c
1
, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
9x+3y+12=0;18x+6y+24=0
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Answer
Correct option is
C
Coincident
The given linear equation are
⇒9x+3y+12=0....eq1
⇒a
1
=9,b
1
=3,c
1
=12
⇒18x+6y+24...eq2
⇒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
⇒
a
2
a
1
=
b
2
b
1
=
c
2
c
1
Hence,the line represented by eq1 and eq2 are coincidents
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