Question

The equation of a line parallel to $x+2y=1$ and passing through the point of intersection of the lines $x-y=4$ and $3x+y=7$ is ?

• A. $x+2y=5$
• B. $4x+8y-1=0$
• C. $4x+8y+1=0$
• D. none of these

Answer 1

Answer: (B)

$4x+8y-1=0$

Let the equation of line parallel to $x+2y=1$ be $y=mx+c$

intersection point of line $x-y=4$ and $3x+y=7$ is given by solving two equation we get $x=\frac{11}{4}$ and $y=\frac{-5}{4}$

from equation $x+2y=1\Rightarrow y=-\frac{1}{2}x+\frac{1}{2}$

we get $m_1=-\frac{1}{2}$

since $y=mx+c$ is parallel to $x+2y=1$

$\therefore m_2=-\frac{1}{2}$

also, $y=mx+c\Rightarrow \frac{-5}{4}=\frac{-1}{2}.\frac{11}{4}+c\Rightarrow c=\frac{1}{8}$

therefore equation of line parallel to $x+2y=1$ is given as

$y=mx+c\Rightarrow y=\frac{-1}{2}x+\frac{1}{8}\Rightarrow 4x+8y-1=0$