a) Each of the inequalities determine the semiplane, first semiplane is shaded in red with solid boundary line (because the inequality has sign ≥), second semiplane is shaded in blue with dashed boundary line (because the inequality has the sign <). The common region represents the solution of this system of two inequalities.
b) Pick a point (10,5) from the shaded region. Since
[tex]5\ge -\dfrac{1}{2}\cdot 10+2\dfrac{1}{2}=-5+2\dfrac{1}{2}=-2\dfrac{1}{2},\\ \\5<\dfrac{1}{5}\cdot 10+6=2+6=8,[/tex]
the coordinates of this point are the solution of the system.
