First slide

Pair of straight lines

Question

If the pair of straight lines $x y - x - y + 1 = 0$ and the line ax+2y-3=0 are concurrent then a =

Moderate

Solution

$x (y - 1) - (y - 1) = 0; (x, y) = (1, 1)$
substitute (1,1) in $a x + 2 y - 3 = 0$
$a (1) + 2 - 3 = 0; a = 1$

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