The number of values of $a$ for which the lines $2 x + y - 1 = 0$ , $a x + 3 y - 3 = 0$ , and $3 x + 2 y - 2 = 0$ are concurrent is

0

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1

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2

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Infinite

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Solution

The correct option is D Infinite
Intersection of $2 x + y - 1 = 0$ and $3 x + 2 y - 2 = 0$ is $(0, 1) .$
$a x + 3 y - 3 = 0$ always passes through $(0, 1) .$
Therefore, there will be infinite values of $a .$

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2 x + y - 1 = 0, a x + 3 y - 3 = 0

3 x + 2 y - 2 = 0

a

2 x + y - 1 = 0 a x + 3 y - 3 = 0 3 x + 2 y - 2 = 0

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