Question

How do you graph the system of inequalities `y<2x + 2`, `y> -x - 1`?

Answer 1

See below.

Explanation:

First graph the equations `y=2x+2` and `y=-x-1`. Use a dashed line as these are `<` and `>` and not `<=` and `>=` inequalities. This will give you the boundary lines.

Test an `(x,y)` coordinate in each section, to see which region is included or excluded.

Looking at graph, test coordinates in Areas A, B , C and D. These coordinates must satisfy both inequalities.

A `(-1 ,3 )`

`-1<2(-1)+3color(white)(888)` TRUE

`-1> -(-1)-1color(white)(888)` FALSE

A is an excluded region.

B`( 1 , 1 )`

`1< 2(1)+2color(white)(888)` TRUE

`1>-(1)-1color(white)(888)` TRUE

B is the included region.

Since we have found included region, we do not need to test any further.