• # question_answer 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)  $x=0$

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 $(-6/5,\,-7/5)$. $\Rightarrow$ $(y-0)+\frac{-7/5-0}{-6/5-0}(x-0)$ $\Rightarrow$ $y=\frac{7}{6}.x$ $\Rightarrow$                          $7x=6y$