Let the equation of the line be x/a + y/b = 1
This passes through (3, 4), therefore 3/a + 4/b = 1
It is given that a + b = 14
⇒ b = 14 – a.
Putting b = 14 – a in (ii), we get 3/a + 4/14 - a = 1
⇒ a2 – 13a + 42 = 0
⇒ (a – 7) (a – 6) = 0
⇒ a = 7, 6 For a = 7, b = 14 – 7 = 7 and for a = 6, b = 14 – 6 = 8.
Putting the values of a and b in (i), we get the equations of the lines
or x + y = 7 and 4x + 3y = 24