(Q.13). Check whether the following pair of equations is consistent. 3x + 4y = 2 and 6x + 8y = 4. Verify by a graphical representation.

3x + 4y - 2 = 0

6x + 8y - 4 = 0

a1
a2
 =
=
1
b1
b2
 =
=
1
c1
c2
 =
-
-
 =
1
Since
a1
a2
 =
b1
b2
 =
c1
c2
 , therefore, they are coincident lines. So, the pair of linear equations are consistent and dependent and have infinitely many solutions
For the equation 3x + 4y = 2
x y =
2 - 3x
4
 		(x,y)
0 y =
2 - 3()
4
 =
1
 		(0,
1
)
2 y =
2 - 3()
4
 = - 		(2,-)
4 y =
2 - 3()
4
 = - 		(4,-)
6 y =
2 - 3()
4
 = - 		(6,-)
For the equation 6x + 8y = 4
x y =
4 - 6x
8
 		(x,y)
0 y =
4 - 6()
8
 =
1
 		(0,
1
)
2 y =
4 - 6()
8
 = - 		(2,-)
4 y =
4 - 6()
8
 = - 		(4,-)
6 y =
4 - 6()
8
 = - 		(6,-)