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

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

The intersection point of the lines $x-2y=1$ 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 lines is $-\frac{3}{4}$.

$\therefore$ Equtaion of required line which passes through $(\frac{7}{5},\frac{1}{5})$ is given by

$y-\frac{1}{5}=-\frac{3}{4}(x-\frac{7}{5})$

$\Rightarrow \frac{3x}{4}+y=\frac{21}{20}+\frac{1}{5}$

$3x+4y=4\times \frac{21+4}{20}$

$\Rightarrow 3x+4y-5=0$ is the required equation of line.