Question

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

(5,1)
(0,0)
(-2,-3)
(2,5)

can you help me with this question and explain how you got the answer please and thank you ! this is very important !!!!!!!!!

Answer 1

The system is

i)
`y \leq (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 (1)/(5) *5=1` True
ii)
`1\ \textgreater \ 4*5-3=20-3=17` Not True

(0, 0)
i)
`0 \leq (1)/(5) *0=0` True
ii)
`0\ \textgreater \ 4*0-3=-3` True

(-2, -3)
i)
`-3 \leq (1)/(5) (-2)= (-2)/(5)= -0.4` True
ii)
`-3\ \textgreater \ 4(-2)-3=-8-3=-11` True

(2, 5)
i)
`5 \leq (1)/(5)*2= (2)/(5) =0.4` Not True
ii)
`5\ \textgreater \ 4*2-3=8-3=5` Not True


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