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)

3x + 4y - 5 = 0

Answer 2

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
$y - \frac{1}{5} = - \frac{3}{4}\left(x - \frac{7}{5}\right)$
$\Rightarrow \frac{3x}{4} + y = \frac{21}{20} + \frac{1}{5}$
$\Rightarrow 3x+ 4y - 5 = 0$