Given the four lines with equations $x + 2y = 3,$ $3x + 4y = 7,$ $2x + 3y = 4,$ and $4x + 5y = 6,$ these lines are:

Find the equation of the line perpendicular to $5x - 2y + 7 = 0$ and passing through the intersection of the lines $y = x + 7$ and $x + 2y + 1 = 0$.

If the sum of squares of all real values of $\alpha$,for which the lines $2x - y + 3 = 0$,$6x + 3y + 1 = 0$,and $\alpha x + 2y - 2 = 0$ do not form a triangle is $p$,then the greatest integer less than or equal to $p$ is $.........$

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 the straight lines $ax + amy + 1 = 0$,$bx + (m + 1)by + 1 = 0$,and $cx + (m + 2)cy + 1 = 0$ $(m \neq 0)$ are concurrent,then $a, b, c$ are in: