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

Dear Student, 
Given lines are
5x +7y -3 = 0    ...(i), and
2x -3y -7 = 0    ...(ii)
Solving (i) and (ii) simultaneously, we get x = 2, y = -1.
Now equation of line passing through (0,0) and (2,-1) is:
$$\begin{gathered} \mathrm{y}-0 = \frac{-1-0}{2-0}\left(\mathrm{x}-0\right) \\ 2\mathrm{y} = -\mathrm{x} \\ \mathrm{x}+2\mathrm{y} = 0 \\ \mathrm{Regards} \end{gathered}$$