The system is
i) [tex]y \leq \frac{1}{5} x[/tex]
ii) [tex]y\ \textgreater \ 4x-3[/tex]
The solutions to this system, are all points (x, y) for which BOTH these 2 inequalities hold.
Check the points separately:
(5, 1)
i) [tex]1 \leq \frac{1}{5} *5=1[/tex] True
ii) [tex]1\ \textgreater \ 4*5-3=20-3=17[/tex] Not True
(0, 0)
i) [tex]0 \leq \frac{1}{5} *0=0[/tex] True
ii) [tex]0\ \textgreater \ 4*0-3=-3[/tex] True
(-2, -3)
i) [tex]-3 \leq \frac{1}{5} (-2)= \frac{-2}{5}= -0.4[/tex] True
ii) [tex]-3\ \textgreater \ 4(-2)-3=-8-3=-11[/tex] True
(2, 5)
i) [tex]5 \leq \frac{1}{5}*2= \frac{2}{5} =0.4[/tex] Not True
ii)[tex]5\ \textgreater \ 4*2-3=8-3=5[/tex] Not True
Answer: (0, 0) and (-2, -3)
