(Q.14). Check whether the equations 2x-3y = 5 and 4x-6y = 15 are consistent. Also verify by graphical representation.

4x - 6y - 15 = 0

2x - 3y - 5 = 0

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

So the equations are inconsistent. They have no solutions and their graph is of parallel lines.

For the equation 4x - 6y = 15
x y =
15 - 4x
-6
 		(x,y)
0 y =
15 - 4()
-6
 =
-
 		(0,-)
3 y =
15 - 4()
-6
 =
-
 		(3,-)
6 y =
15 - 4()
-6
 =
(6,)
For the equation 2x - 3y = 5
x y =
5 - 2x
-3
 		(x,y)
1 y =
5 - 2()
-3
 = - 		(1,-)
4 y =
5 - 2()
-3
 = 		(4,)
7 y =
5 - 2()
-3
 = 		(7,)