Solve the following system of linear inequalities: $2(x-6) < 3x-7$ and $11-2x < 6-x$.

The shaded region in the figure is the solution set of the inequations:

Find the linear inequalities for which the shaded region in the given figure is the solution set.

Show that the solution set of the following system of linear inequalities is an unbounded region: $2x + y \geq 8$,$x + 2y \geq 10$,$x \geq 0$ and $y \geq 0$.

Show that the following system of linear inequalities has no solution: $x + 2y \leq 3$,$3x + 4y \geq 12$,$x \geq 0$,and $y \geq 1$.

Solve the following system of inequalities graphically: $x+y < 2, x > 0, y > 1$.