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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. - CBSE (Arts) Class 11 - Mathematics

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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.

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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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.
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