Question

Find the equation of the line passing through the origin and the point of intersection of the lines 5x + 7y = 3 and 2x - 3y = 7.

Answer 1

The point of intersection of lines,

$5x+7y=3$...(1) and

$2x-3y=7$...(2)

Solving (1) and (2) , we get,

$(x,y)=(2,-1)$

Therefore the equation of line passing through $(0,0)$ and $(2,-1)$ is

$(y-0)=\frac{-1-0}{2-0}(x-0)$

$2y=-x$

$\therefore x+2y=0$ is the required equation