Question

How many pairs of x and y satisfy the given equation 4x+6y=16 and 6x+9y=24?

Answer 1

Solution :

Equation ( i ) -> 4x + 6y = 16 => 2x + 3y = 8
Equation ( ii ) -> 6x + 9y = 24 => 2x + 3y = 8 

Since Equation ( i ) ≡ Equation ( ii ), both lines are same, i.e., they have infinitely many solns. for real ( x , y )

Answer 2

4x+6y = 16

6x+9y = 24

a₁ = 4     b₁ = 6     c₁=16                      ...............(1)

a₂ = 6     b₂ = 9     c₂=24                      ...............(2)

Then,

Dividing (1) by (2)

⇒ 4/6 = 6/9 = 16/24

⇒ 1/3 = 1/3 = 1/3

As a₁/a₂ = b₁/b₂ = c₁/c₂ 

Hence they give out infinitely many solutions.
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