Without actually solving the simultaneous equation given, examine whether it has unique solution, no solution or infinitely many solutions. (i) x + 3y + 4 = 0 ; 2x + 6y – 3 = 0

Solution:

Comparing  x + 3y + 4 = 0  with a1x + b1y + c1 = 0 , We get

a1 = 1; b1 = 3, c1 = 4

Comparing 2x + 6y – 3 = 0 with   a2x + b2 y + c2 = 0, We get

a2 = 2, b2 = 6, c2 = - 3

a1
=
1


a2

2



b1
=
3
=
1
b2

6

2

c1
=
4
=
-4
c2

-3

3

Here,
1
=
b1
c1



a2

b2

c2




the given two lines are parallel lines
∴ they have no solution.

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