graph the system of inequalities

Question

how do I graph the system of inequalities using  y <= 3/2 + 3,   2x + y < 10,  y > -1.  Please solve and show

 

all steps.  Is it easy to shade each half-plane solution?

Answer 1

 Y≤3/2X + 3

 

 

 

  First graph the line Y = 3/2 X + 3

 

       The intercept points are : ( 0 ,3 )  ,  ( -2 , 0 )

 

      After drawing test a point to the right or left of the line.

 

       ( 0, 0 )

 

             0 ≤ 0 + 3 , therefore the region to the right of the ( -2, 0 ) is the solution, mark it with dash with shade as solution .

    Since there is ≤ the line has to be solid, meaning the points on the lines are the solution.

    without the  = sign then the line would have been drawn as dashed lines.