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

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

Solve the following system of linear inequalities: $3x + 2y \geq 24$,$3x + y \leq 15$,$x \geq 4$.

Solve the following system of inequalities graphically:
$x + 2y \leqslant 8$ ..... $(1)$
$2x + y \leqslant 8$ ..... $(2)$
$x \geqslant 0$ ..... $(3)$
$y \geqslant 0$ ..... $(4)$

The solution set of the constraints $2x + 3y \leq 6$,$5x + 3y \leq 15$,$x \geq 0$,and $y \geq 0$ does not include which of the following points?

The shaded figure given below is the solution set for the linear inequations. Choose the correct option.