Question

Find the equation of a line passing through the intersection of `"x"/10 + "y"/5` = 14 and `"x"/8 + "y"/6` = 15 and perpendicular to the line x - 2y = 5

Answer 1

`"x"/10 + "y"/5` = 14 ⇒ x + 2y = 140......(1)

`"x"/8 + "y"/6` = 15 ⇒ 3x + 4y = 360........(2)

(1) can be rewritten as 2x + 4y = 280......(3)

(2) can be rewritten as 3x _ 4y = 360........(4) 

subtracting (3) from (4), we get

x = 80

y = 30

Point of intersection of (1) and (2) is (80,30)

slope of x - 2y = 5 is`1/2`

Equation of required line is `("y" - "y"_1)/("x" - "x"_1)` = m

`("y" - 30)/("x" -80)` = -2

⇒ -2x + 160 = y - 30

⇒ 2x + y = 190