Given: - Two equation x + 2y = 5 and 3x + 6y = 15

Tip: - We know that

For a system of 2 simultaneous linear equation with 2 unknowns

(iv) If D ≠ 0, then the given system of equations is consistent and has a unique solution given by

(v) If D = 0 and D₁ = D₂ = 0, then the system is consistent and has infinitely many solution.

(vi) If D = 0 and one of D₁ and D₂ is non – zero, then the system is inconsistent.

Now,

We have,

x + 2y = 5

3x + 6y = 15

Lets find D

⇒

⇒ D = – 6 – 6

⇒ D = 0

Again, D₁ by replacing 1^st column by B

Here

⇒

⇒ D₁ = 30 – 30

⇒ D₁ = 0

And, D₂ by replacing 2^nd column by B

Here

⇒

⇒ D₂ = 15 – 15

⇒ D₂ = 0

So, here we can see that

D = D₁ = D₂ = 0

Thus,

The system is consistent with infinitely many solutions.

Let

y = k

then,

⇒ x + 2y = 5

⇒ x = 5 – 2k

By changing value of k you may get infinite solutions