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The pair of equations $x + 2 y + 5 = 0$ and $− 3 x − 6 y + 1 = 0$ and have

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Detailed Solution

Given equations are

x + 2 y + 5 = 0

and

− 3 x − 6 y + 1 = 0

.
We know that any of two linear equations of the form

a 1 x + b 1 y + c 1 = 0

and

a 2 x + b 2 y + c 2 = 0

will have no solution if and only if

a 1 a 2 = b 1 b 2 ≠ c 1 c 2

.
On comparing the above equations with

a 1 x + b 1 y + c 1 = 0

and

a 2 x + b 2 y + c 2 = 0

, we get

a 1 = 1, b 1 = 2, c 1 = 5

and

a 2 = − 3, b 2 = − 6, c 2 = 1

.
Let us use the condition for the ratios of coefficients.

⇒ − 13 = − 13 ≠ 51

So, the given system of equations have no solution.
The correct option is (1).

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