Question

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

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

Answer 1

Answer: (C)

The intersection point of lines $x-2y=1$ and $x+3y=2$ is $\left(\frac{7}{5},\frac{1}{5}\right)$
Since, required line is parallel to $3x+4y=0.$
Therefore, the slope of required line is $-\frac{3}{4}$
$\therefore$ Equation of required line which passes throught $\left(\frac{7}{5},\frac{1}{5}\right)$ is given by
$y-\frac{1}{5}=-\frac{3}{4}\left(x-\frac{7}{5}\right)$
$\Rightarrow \frac{3x}{4}+y=\frac{21}{20}+\frac{1}{5}$
$\Rightarrow 3x+4y-5=0$