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

$L_1$ and $L_2$ are two lines having slopes $2$ and $-\frac{1}{2}$ respectively. If both $L_1$ and $L_2$ are concurrent with the lines $x-y+2=0$ and $2x+y+3=0$,then the sum of the absolute values of the intercepts made by the lines $L_1$ and $L_2$ on the coordinate axes is:

If the lines $4x + 3y - 1 = 0$,$x - y + 5 = 0$,and $kx + 5y - 3 = 0$ are concurrent,then $k=$

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 line parallel to the $x$-axis passing through the intersection of the lines $ax + 2by + 3b = 0$ and $bx - 2ay - 3a = 0$, where $(a, b) \neq (0, 0)$, 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