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Write the condition for the system of linear equations $a x + b y = c$ and $p x + q y = r$ to have a unique solution.

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a q ≠ p b

a q = p b

p q ≠ p b

a q ≠ a b

answer is A.

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Detailed Solution

We are given.

a x + b y = c p x + q y = r

Two lines

a x_{1} + {by}_{1} + c_{1} = 0

and

a x_{2} + {by}_{2} + c_{2} = 0

have unique solution only if

\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

.
Since, the equations have a unique solution,
So,

a p ≠ b q a q ≠ p b

The condition is

a q ≠ p b

.
Hence, option 1 is correct.

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