Find the equation of the straight line which passes through the point $\left(1,1\right)$ and the point of intersection of the lines $3x+2y=0$ and $x-2y=0$.

Find the equation of the line through the point of intersection of $x+2y=5$ and $x-3y=7$, and passing through the point $\left(0,0\right)$ .

Find the equation of the line through the point of intersection of $x+2y=5$ and $x-3y=7$, and passing through the point $\left(0,-1\right)$ .

Find the equation of the line through the intersection of $5x-3y=1$ and $2x+3y-23=0$, and perpendicular to the line whose equation is $x=0$ .

Find the equation of the line through the intersection of $5x-3y=1$ and $2x+3y-23=0$, and perpendicular to the line whose equation is $y=0$

Find the equation of the line through the intersection of $5x-3y=1$ and $2x+3y-23=0$, and perpendicular to the line whose equation is:

$5x-3y-1=0$