Let u ≡ x + y + 9 = 0 and v ≡ 2x + 3y + 1 = 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 + 9) + k(2x + 3y + 1) = 0 ……(i)
⇒ x + y + 9 + 2kx + 3ky + k = 0
⇒ (1 + 2k)x + (1 + 3k)y + 9 + k = 0
But, x-intercept of this line is 1
⇒\(\frac {-(9+k)}{1+2k}\)
⇒ -9 – k = 1 + 2k
⇒ k = -10/3
Substituting the value of k in (i), we get (x + y + 9) + (-10/3) (2x + 3y + 1) = 0
⇒ 3(x + y + 9) – 10(2x + 3y + 1) = 0
⇒ 3x + 3y + 27 – 20x – 30y – 10 = 0
⇒ -17x – 27y+ 17 = 0 ⇒ 17x + 27y – 17 = 0, which is the equation of the required line.
