Answer :

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 D_{1} = D_{2} = 0, then the system is consistent and has infinitely many solution.

(vi) If D = 0 and one of D_{1} and D_{2} 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, D_{1} by replacing 1^{st} column by B

Here

⇒

⇒ D_{1} = 30 – 30

⇒ D_{1} = 0

And, D_{2} by replacing 2^{nd} column by B

Here

⇒

⇒ D_{2} = 15 – 15

⇒ D_{2} = 0

So, here we can see that

D = D_{1} = D_{2} = 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

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