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.