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Question
Find the equation of the line passing through the point of intersection of lines x + y − 2 = 0 and 2x − 3y + 4 = 0 and making intercept 3 on the X-axis
Solution
Let u ≡ x + y – 2 = 0 and v ≡ 2x – 3y + 4 = 0
Equation of the line passing through the point of intersection of lines u = 0 and v = 0 is given by u + kv = 0.
∴ (x + y – 2) + k(2x – 3y + 4) = 0 ...(i)
But, x-intercept of a line is 3.
∴ It passes through (3, 0).
Substituting x = 3 and y = 0 in (i), we get
(3 + 0 – 2) + k(6 – 0 + 4) = 0
∴ 1 + 10k = 0
∴ k = `(-1)/10`
Substituting the value of k in (i), we get
`(x + y - 2) + ((-1)/10)(2x - 3y + 4)` = 0
∴ 10(x + y – 2) – (2x – 3y + 4) = 0
∴ 10x + 10y – 20 – 2x + 3y – 4 = 0
∴ 8x + 13y – 24 = 0, which is the equation of the required line.
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