(i) x–3y–3=0
3x–9y–2=0
Comparing these with pair of equations of the form a
1
x+b
1
y+c
1
=0
and a
2
x+b
2
y+c
2
=0,
a
2
a
1
=
3
1
,
b
2
b
1
=
−9
−3
=
3
1
,
c
2
c
1
=
2
3
∵
a
2
a
1
=
b
2
b
1
=
c
2
c
1
, the lines have no solution.
(ii) 2x+y=5
3x+2y=8
a
2
a
1
=
3
2
,
b
2
b
1
=
2
1
,
c
2
c
1
=
8
5
∵
a
2
a
1
=
b
2
b
1
, the lines have unique solution.
(iii) 3x−5y=20
6x−10y=40
a
2
a
1
=
6
3
=
2
1
,
b
2
b
1
=
−10
−5
=
2
1
,
c
2
c
1
=
40
20
=
2
1
∵
a
2
a
1
=
b
2
b
1
=
c
2
c
1
, the lines have infinitely many solution.
(iv) x−3y−7=0;3x−3y−15=0
a
2
a
1
=
3
1
,
b
2
b
1
=
−3
−3
=1,
c
2
c
1
=
15
7
∵
a
2
a
1
=
b
2
b
1
, the lines have unique solution.