graph system of inequalites

Question

How do I solve and graph this system of inequalities?

 

                  y<= 3/2x + 3

                  -y < 2x

Answer 1

First Graph the

  

    Y ≤ 3/2 X +3

 

        Graph the Y = 3/2 X +3

 

           From ( 0,3 ) go 3 unit up and 2 units to the right , reach point ( 2,6), connect ( 0,3) to ( 2,6) and

           extend , line is solid.

        

              The X - intercept will be ( -2, 0).

             

              Test  point ( 0,0 )

 

               0 ≤ 3/2( 0) +3    true; shade area of the line to the right of ( 0, -2).

 

               Now graph  - Y < 2x , Y > -2x

 

                 Draw Y = -2x

                 

                   Test : (0, 3)    - y < 2X

                 

                 The solution for -Y< 2X  is to the right of the line Y = -2X , is drawn in dash lines.

 

                  The common solution will be to the right of the point ( 0, 3).

               

Answer 2

Drawing lines when you don't know how far apart or what direction they go is the blind way to go about this. I like to find the x and y intercepts and then draw a line between the two.

 

y <= 3/2x + 3

--> (0,3) y intercept and (-2,0) x intercept

-y < 2x can be rewritten by multiplying both sides by -1 (and flipping the inequality):

y> -2x

 

or adding -2x and y to both sides. -2x < y

I do both for good measure.

 

This equation has the same point for x and y intercept.  I like to use a x point from the other equation as a starting point for the line.

so we have (0,0) x, y intercept and (-2, 4). At this point you want to shade *under* the first equation and *over* the second equation.