Solve the following pair of linear equations graphically:

$x+2y=8, 2x-3y=2$

Also, shade the triangular region formed by the lines obtained in the graph and y-axis.

Solve the following system of linear equations graphically:

$2x-3y = 1, 3x-4y=1$

Does the point $(3, 2)$ lie on any of the lines? Write its equation.

Solve graphically the pair of equations $2x+3y=11 \text{and} 2x-4y=-24$. Hence find the value of $m$, given that the line represented by $y=mx+3$ passes through the intersection of the given pair.

Draw the graphs of the equations $x-y+1=0 \text{and} 3x+2y-12=0$. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Draw the graphs of the pair of linear equations $x-y+2=0$ and $4x-y-4=0$. Calculate the area of the triangle formed by the lines so drawn and the x-axis.

 Draw the graph of the pair of equations $2x+y=4 \text{and} 2x-y=4$. Write the coordinates of the vertices of the triangle formed by these lines and the y-axis. Also find the area of this triangle.

Draw the graph of the following pair of linear equations :

$x+3y=6$ and $2x-3y=12$

Find the area of triangle formed with the given lines and the line $x=0$,

Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are

$y=x, y=2x, x+y=6$

A triangle is formed by the lines $x+2y-3=0, 3x-2y+7=0$ and $y+1=0$. Find graphically the coordinates of the vertices of the triangle.