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, a­1 = b1 ≠ c1 a2 b2 c2

∴ the given two lines are parallel lines

∴ they have no solution.