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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.
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Solution
Given lines
3x + y = 2 …(i)
2x – y = 3 …(ii)
By combining equations (i) and (ii),
5x = 5 or x = 1
∴ y = 2 – 3x = 2 – 3 = –1
∴ The lines containing equations (i) and (ii) intersect at the point (1, –1).
The third line px + 2y – 3 = 0 also passes through this point, hence (1, –1) will satisfy this equation.
p × 1 + 2 × ( –1) – 3 = 0
p – 2 – 3 = 0
∴ p = 5
Thus, the required value of p is 5.
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