(Q.28). Check whether the following equations are consistent or inconsistent. Solve them graphically

2x – 3y = 8

4x – 6y = 9

Given: 2x – 3y = 8

4x – 6y = 9

a1
a2
 =
=
1
;
b1
b2
 =
-
-
 =
1
;
c1
c2
 =
∴
a1
a2
 =
b1
b2
 ≠
c1
c2

Lines are inconsistent and have no solution.

2x – 3y = 8
x y ( x, y)
1 - ( 1, -)
7 ( 7, )
4x – 6y = 9
x y ( x, y)
0
-
(0,
-
 ) ⇒ ( 0 , -)
6
(6,
) ⇒ ( 6 , )

The lines are and no solution exists.