What is linear programming? - Inequalities

Find the maximal and minimal value of $z=2x+3y$ subject to the following constraints:

$y \geq x+2$
$y \leq 3x$
$y \leq -2x+20$

Given the following constraints, find the maximal and minimal value of $z=5x+6y$.

$x \geq 0$
$y \geq 0$
$x-6 \leq 0$
$-x+y \leq 6$
$x+y \leq 8$
$\frac{1}{2}x+y \geq 3$