Question

How do you graph the system `x+4y<8` and `3x-y>4`?

Answer 1

First consider the boundary lines:
`color(white)("XXXX")` `x+4y = 8`
`color(white)("XXXX")` `color(white)("XXXX")`this has obvious intercept points `(0,2)` and `(8,0)`
and
`color(white)("XXXX")` `3x-y=4`
`color(white)("XXXX")` `color(white)("XXXX")`with points `(0,-4)` and `(1,-1)`

We can use the boundary line points for each of the inequalities to draw their lines and then compare `(x,y)=(0,0)` to each of the inequalities to determine which side of each line is to be included.
`color(white)("XXXX")`For example `0+4(0)< 8`
`color(white)("XXXX")`so `(0,0)` should be on the included side of `x+4y < 8`