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. $5x-7y+!8=0$
• C. $5x-5y+18=0$
• D. $x-y+5=0$

Answer 1

Answer: (C)

$5x-5y+18=0$

$x+2y-3=0$........................(i)

$2x-y+5=0$.......................(ii)

$1\times$ (i)+$2\times$ (ii), we get

$\Rightarrow 5x+7=0$

$\Rightarrow x=\frac{-7}{5}$

putting value of $x$ in (i), we get

$\frac{-7}{5}+2y-3=0\Rightarrow y=\frac{11}{5}$

$x=\frac{-7}{5},y=\frac{11}{5}$

and slope of $y-x+10=0\Rightarrow y=(x-10)$ is $=1$

Therefore, Equation of the line will be,

$(y-\frac{11}{5})=(x-\frac{-7}{5})\Rightarrow 5y-11=5x+7\Rightarrow 5x-5y+18=0$

Therefore, Answer is $C$