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

1 Answer
Somebody N.
Dec 8, 2017

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.

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