Question

Find the value of p so that the three lines $3x + y - 2 = 0, px + 2y - 3 = 0$ and $2x - y - 3 = 0$ may intersect at one point

Answer 1

The equations of the given lines are
$3x + y - 2 = 0 … (1)$
$px + 2y - 3 = 0 … (2)$
$2x - y - 3 = 0 … (3)$

On solving equations (1) and (3), we obtain
$x = 1$ and $y = -1$

Since these three lines may intersect at one point, the point of intersection of lines (1) and (3) will also satisfy line (2).
$p (1) + 2 (-1) - 3 = 0$
$p - 2 - 3 = 0$
$p = 5$

Thus, the required value of p is 5.