#### Question

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

#### Solution

The equations of the given lines are

3*x* + *y* – 2 = 0 … (1)

*px *+ 2*y* – 3 = 0 … (2)

2*x *– *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.

Is there an error in this question or solution?

Solution 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. Concept: Slope of a Line.