Question

The equation of straight line through the intersection of the lines $x-2y=1$ and $x+3y=2$ and parallel to $3x+4y=0$ is

• A. $3x+4y+5=0$
• B. $3x+4y-10=0$
• C. $3x+4y-5=0$
• D. $3x+4y+6=0$

Answer 1

The correct option is C $3x+4y-5=0$

The intersection point of line $x-2y=1$ and $x+3y=2$ is $(\frac{7}{5},\frac{1}{5})$.
Since, required line is parallel to $3x+4y=0$
$\therefore$ The slope of required line $=-\frac{3}{4}$
Now, equation of required line which passes through $(\frac{7}{5},\frac{1}{5})$ and slope $-\frac{3}{4}$, is
$y-\frac{1}{5}=-\frac{3}{4}(x-\frac{7}{5})$
$\Rightarrow y+\frac{3x}{4}=\frac{21}{20}+\frac{1}{5}$
$\Rightarrow 4y+3x=4\left(\frac{25}{20}\right)$
$\Rightarrow 3x+4y-5=0$