Find the coordinates of the vertcies of the figure formed by 5x=4y<20, y<2x+3, and x-3y<4

Answer 1

I suspect a typo in 5x=4y<20

Once you have fixed that, solve them in pairs, using the = sign
e.g.
solve y = 2x+3 and x- 3y = 4
subbint the first into the 2nd:
x - 3(2x+3) = 4
x - 6x - 9 = 4
x = -13/5
y = -26/5 + 3 = -11/5

So one vertex is (-13/5 , -11/5)

check: Bottom left vertex of the graph
https://www.wolframalpha.com/input/?i=graph+5x%2B4y%3D20%2C+y%3D2x%2B3%2C++x-3y%3D4