The equation of the line passing through the point of intersection of the lines $3x - y = 5$ and $x + 3y = 1$ and making equal intercepts on the axes is

Statement $(A)$: If $3a - 2b + 5c = 0$,then the line $ax + by + c = 0$ is always concurrent at a point.
Reason $(R)$: If $L_1 = 0$ and $L_2 = 0$ are two lines,then the family of lines $L_1 + \lambda L_2 = 0$ is concurrent at the intersection of $L_1$ and $L_2$.

For what values of $\theta$ are the points $(1, 1), (0, \sec^{2}\theta), (\csc^{2}\theta, 0)$ collinear?

If the lines $2x + y - 3 = 0$,$3x + 2y - 2 = 0$,and $kx - 3y - 23 = 0$ are concurrent,then the roots of the equation $6x^2 - 7x + k = 0$ are

If the lines $ax + by + c = 0$,$bx + cy + a = 0$,and $cx + ay + b = 0$ are concurrent,then:

Let $C$ be the centroid of the triangle with vertices $(3, -1), (1, 3),$ and $(2, 4).$ Let $P$ be the point of intersection of the lines $x + 3y - 1 = 0$ and $3x - y + 1 = 0.$ Then the line passing through the points $C$ and $P$ also passes through the point