(Q.17). Check each of the given systems of equations to see if it has a unique solution, infinitely many solutions or no solution. Solve them graphically.

3x + 2y = 6

6x + 4y = 18

From the given pair of equations,

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

∴ The lines are parallel and hence no solution.

3x + 2y = 6

2y = 6 – 3

y =
6 - 3
3x + 2y = 6
x y =
6 - 3x
2
 		(x,y)
0 (0,)
2 (2,)

6x + 4y = 18

4y = 18 – 6

y =
18 - 6
6x + 4y = 18
x
y =
18 - 6x
4
(x,y)
3 (3,)
-1 (-1,)