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State whether the following statement is true or false.

The system of linear equations $− 3 x − 6 y + 1 = 0$ and $x + 2 y + 5 = 0$ have no solution.

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True

False

answer is A.

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Detailed Solution

The given equations are

− 3 x − 6 y + 1 = 0

x + 2 y + 5 = 0

We know that, a pair of linear equations

a 1 x + b 1 y + c 1 = 0 a 2 x + b 2 y + c 2 = 0

has no solution if ( and only if)

a 1 a 2 = b 1 b 2 ≠ c 1 c 2

Since we have,

− 3 x − 6 y + 1 = 0

x + 2 y + 5 = 0

∴ a 1 a 2 = − 13, b 1 b 2 = − 26 = − 13, and c 1 c 2 = 15

⇒ a 1 a 2 = b 1 b 2 ≠ c 1 c 2

Thus, the given equations

a x + b y − c = 0

and

p x + q y − r = 0

have no solution.
Therefore the given statement is true.
Hence option (1) is correct.

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