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

Let $a, b, c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4ax + 2ay + c = 0$ and $5bx + 2by + d = 0$ lies in the fourth quadrant and is equidistant from the two axes,then:

Find the equation of the line passing through the intersection of the lines $4x - 3y - 1 = 0$ and $5x - 2y - 3 = 0$ and parallel to the line $2x - 3y + 2 = 0$.

The equation of the line passing through the point of intersection of the lines $2x + 3y + 6 = 0$ and $3x - y - 13 = 0$ and parallel to the line $3x - 4y + 5 = 0$ is

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

If the three lines $p_1x + q_1y = 1$,$p_2x + q_2y = 1$,and $p_3x + q_3y = 1$ are concurrent,then the points $(p_1, q_1)$,$(p_2, q_2)$,and $(p_3, q_3)$ are: