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Consider the family of lines (x+y-1)+lam...

Consider the family of lines `(x+y-1)+lamda(2x+3y-5)=0` and `(3x+2y-4)+mu(x+2y-6)=0`. Equation of a line that belongs to both the family is
(A) `x-2y-8=0`
(B) `x-2y+8=0`
(C) `2x+y-8=0`
(D) `2x-y-8=0`

Text Solution

Verified by Experts

First, we will solve equations,
`x+y-1 = 0->(1)` and `2x+3y-5 = 0->(2)`
Multiplying (1) by 2 and subtracting it from (2), we get,
`2x+3y-2x-2y = 5 -2 => y = 3`
Putting `y = 3` in (1),
`x+3-1 = 0 => x = -2`
So, point of intersection of first family of line is `(-2,3)`.
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