Find the equation of the line passing through the intersection of the lines $x + y - 3 = 0$ and $2x - y + 1 = 0$ and the point $(2, -3)$.

The straight line that passes through the point of intersection of the straight lines $x + 2y - 10 = 0$ and $2x + y + 5 = 0$ is:

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

If the straight lines $2x - y + 1 = 0$,$4x + y + 2 = 0$,and $x + y - k = 0$ are concurrent,then $k$ equals

If $\pi / 3$ is the angle between the straight lines $px + qy + r = 0$ and $x \sin \alpha + y \cos \alpha = r$ $(r \neq 0)$ which meet at a point $A$,and the straight line $x \cos \alpha - y \sin \alpha = 0$ also passes through the point $A$,then:

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: