Question

Which point represents a solution to the system y ≤ (1)/(5)x y > 4x-3 select all that apply

Answer 1

The system is 

i) $y \leq \frac{1}{5} x$
ii) $y\ \textgreater \ 4x-3$

The solutions to this system, are all points (x, y) for which BOTH these 2 inequalities hold.

Check the points separately: 

(5, 1)
i) $1 \leq \frac{1}{5} *5=1$ True
ii) $1\ \textgreater \ 4*5-3=20-3=17$ Not True

(0, 0)
i) $0 \leq \frac{1}{5} *0=0$ True
ii) $0\ \textgreater \ 4*0-3=-3$ True

(-2, -3)
i) $-3 \leq \frac{1}{5} (-2)= \frac{-2}{5}= -0.4$ True
ii) $-3\ \textgreater \ 4(-2)-3=-8-3=-11$ True

(2, 5)
i) $5 \leq \frac{1}{5}*2= \frac{2}{5} =0.4$ Not True
ii)$5\ \textgreater \ 4*2-3=8-3=5$ Not True


Answer: (0, 0) and (-2, -3)