Show that each of the following systems of linear equations is inconsistent:

3x + y = 5

– 6x – 2y = 9

Given: - Two equation 3x + y = 5 and – 6x – 2y = 9

Tip: - We know that

For a system of 2 simultaneous linear equation with 2 unknowns

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

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

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

Now,

We have,

3x + y = 5

– 6x – 2y = 9

Lets find D

⇒

⇒ D = – 6 – 6

⇒ D = 0

Again, D₁ by replacing 1^st column by B

Here

⇒

⇒ D₁ = – 10 – 9

⇒ D₁ = – 19

And, D₂ by replacing 2^nd column by B

Here

⇒

⇒ D₂ = 27 + 30

⇒ D₂ = 57

So, here we can see that

D = 0 and D₁ and D₂ are non – zero

Hence the given system of equation is inconsistent.