The line passing through the point of intersection of `x + y = 2,x-y = 0` and is parallel to `x + 2y =5`, is

Options

A. x+2y=1
B. x+2y=2
C. x+2y=4
D. x+2y=3

Answer

D

Explanation

The line passing through the intersection of two given lines be
(x+y-2) `+ lamda ` (x-y) =0
` or (1+lamda) x + (1-lamda) y-2=0`
Since it is parallel to x +2y =5
`- ((1+lamda))/((1-lamda)) = -1/2 `
` 2 +2 lamda = 1-lamda`
` Rightarrow lamda = -1/3`
On putting ` lamda = -1/3 ` in Eq. (i) we get
`2/3 x +4/3 y -2-0`
x+2y =3