Question

The equation of the line passing through $(0,0)$ and intersection of $3x-4y=2$ and $x+2y=-4$ is

• A. $7x=6y$
• B. $6x=7y$
• C. $5x=8y$
• D. $x=0$

Answer 1

Answer: (A)

$7x=6y$

Answer 2

The correct answer is A:$7x=6y$
Given lines, $3x-4y=2$ ..(i)
$x+2y=-4$ ..(ii)
Intersection point of these line is
$3(-4-2y)-4y=2$ $-12-6y-4y=2$
$10y=-14\,\,\,\,\Rightarrow \,\,\,y=-7/5$ and $x=-4-2(-7/5)=-4+14/5$
$x=-6/5$
Intersection point is
$(-6/5,\,\,-7/5)$ .
Now, the equation of the line which passes through the points
$(0,0)$ and $(-6/5,\,-7/5)$ .
⇒$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$
$\Rightarrow$ $(y-0)+\frac{-7/5-0}{-6/5-0}(x-0)$
$\Rightarrow$ $y=\frac{7}{6}.x$
$\Rightarrow$ $7x=6y$