(Q.16). 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.

x + 2y = 6

2x + 4y = 12

From the given pair of equations,

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

∴ The lines are dependent and have many solutions.

x + 2y = 6

2y = 6 –

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

2x + 4y = 12

4y = 12 – 2

y =
12 - 2
y =
6 -
2x + 4y = 12
x
y =
12 - 2x
4
(x,y)
0 (0,)
6 (6,)