Question

How do you graph `0<=x-y<=2`?

Answer 1

See below

Explanation:

`0<=(x-y)<=2`

This represents two inequalities, namely:

`0<=(x-y)` (i)

and

`(x-y)<=2` (ii)

First let's consider (i):
`0<=(x-y) -> -y+x>=0`

`-y>=-x`

`y<=x`

This inequality is represented graphically by all points on the `xy-`plane on or under the line `y=x`.

Similarly for (ii):

`(x-y)<=2 -> -y+x<= 2`

`-y<=-x+2`

`y>=x-2`

This inequality is represented graphically by all points on the `xy-`plane on or above the line `y=x-2`.

Combining these two results produces the graph below.

graph{(x-y)(x-y-2)<=0 [-11.25, 11.25, -5.63, 5.62]}