Find the value of p so that the three lines 3x + y – 2 = 0,

Question:

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

Solution:

The equations of the given lines are

3x + y – 2 = 0 … (1)

px + 2y – 3 = 0 … (2)

2– y – 3 = 0 … (3)

On solving equations (1) and (3), we obtain

= 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.

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