The equation of the line passing through the point of intersection of the lines $4x - 3y - 1 = 0$ and $5x - 2y - 3 = 0$ and parallel to the line $2y - 3x + 2 = 0$ is:

The value of $k$ such that the lines $2x - 3y + k = 0$,$3x - 4y - 13 = 0$,and $8x - 11y - 33 = 0$ are concurrent,is

If $(x_1, y_1)$ are the roots of $x^2 + 8x - 20 = 0$,$(x_2, y_2)$ are the roots of $4x^2 + 32x - 57 = 0$ and $(x_3, y_3)$ are the roots of $9x^2 + 72x - 112 = 0$,then the points $(x_1, y_1), (x_2, y_2)$ and $(x_3, y_3)$:

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

The equation of the line parallel to the $y$-axis and passing through the point of intersection of the lines $ax + by + c = 0$ and $a'x + b'y + c' = 0$ is:

The points $\left( 0, \frac{8}{3} \right)$,$(1, 3)$,and $(82, 30)$