Question

What is the equation of the line passing through the point of intersection of the lines `x+2y-3=0` and `2x-y+5=0` and parallel to the line `y-x+10=0` ?
A. `7x-7y+18=0`
B. `5x-7y+18=0`
C. `5x-5y+18=0`
D. `x-y+5=0`

Answer 1

Correct Answer - C
Given lines,
`x+2y-3=0` ...(1)
`2x-y+5=0` ...(2)
`{:((1)xx2 implies" "2x+4y-6=0),((2) implies" "2x-y+5=0),(" "cancel((-))" (+) (-)"),(" "bar(5y-11=0implies y=11/5)):}`
`(1)implies x+2(11/5)-3=0`
`implies x+22/5-3=0 implies x+7/5=0 implies x= (-7)/5`.
Given, the required line is parallel to `y-x+10=0`.
`implies y=x-10`
`implies y=(1) x+(-10)`
`:.` Slope `(m)=1`
`:.` Required line with slope 1 and passing through
`((-7)/5, 11/5)` is
`y-y_(1)=m(x-x_(1))`
`implies y-11/5=1 (x+7/5)`
`implies 5y-11=5x+7 implies 5x-5y+18=0`.