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

Answer 1

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.