Question

How do you graph the system `x>=2` and `y+x<=5`?

Answer 1

Consider the equations
`color(white)("XXXXX")` `x=2` which is a vertical line through `(2,0)`
`color(white)("XXXXX")` `color(white)("XXXXX")` `x>=2` will be all points on this line plus all points to the right of it

`color(white)("XXXXX")` `y+x=5` which is a line through the points `(0,5) and (5,0)`
`color(white)("XXXXX")` `color(white)("XXXXX")` `y+x<=5` will be all points on this line and all points below and to the left of it.

`x>=2 and y+x<=5` will be the intersection of these two areas