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:

Let $\alpha, \beta, \gamma$ be three non-zero real constants and $a, b, c$ be three arbitrary real numbers which satisfy $\alpha a + \beta b + \gamma c = 0$. Then the point of concurrence of the family of lines $ax + by + c = 0$ is

If the lines $4x + 3y = 1$,$y = x + 5$,and $5y + bx = 3$ are concurrent,then the value of $b$ is:

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

If the lines $2x + y - 3 = 0$,$3x + 2y - 2 = 0$,and $kx - 3y - 23 = 0$ are concurrent,then the roots of the equation $6x^2 - 7x + k = 0$ are

If the lines $x + 2ay + a = 0$,$x + 3by + b = 0$,and $x + 4cy + c = 0$ are concurrent,then $a, b,$ and $c$ are in which of the following?