Find the coordinates of the vertices of a triangle, the equations of whose sides are $x+y-4=0,2x-y+3=0\text{ and }x-3y+2=0$

Find the area of the triangle formed by the lines $y=m_{1}x+c_1,y=m_{2}x+c_2\text{ and }x=0$.

Find the area of the triangle formed by the lines $x+y-6=0,x-3y-2=0\text{ and }5x-3y+2=0$

Classify the following pair of lines as coincident, parallel or intersecting:

$2x+y-1=0$ and $3x+2y+5=0$.

Classify the following pair of lines as coincident, parallel or intersecting: $x-y=0 \mathrm{and} 3 x-3 y+5=0$