For what value of $a$ are the lines $x = 3$,$y = 4$,and $4x - 3y + a = 0$ concurrent?

The least positive value of $t$,so that the lines $x=t+\alpha, y+16=0$ and $y=\alpha x$ are concurrent,is

If the system of equations $2x + 3y = -1$,$3x + y = 2$,and $\lambda x + 2y = \mu$ is consistent,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:

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 passing through the point of intersection of the lines $x-3y+2=0$ and $2x+5y-7=0$ and perpendicular to the line $3x+2y+5=0$ is: