Topic 5.3        (Systems of Inequalities)

It is a good idea to read the sections on Inequalities in the PAN

Sample problem

Graph the system of inequalities:

     y    >    x    -    4    &    x    +    2y    <    6        Put each equation in the form

     y    =    x    -    4          2y    =    -x    +    6           y    =    mx    +    b.

                                       y    =    (-1/2) x    +    3

           m    =    1/1             m    =    -1/2

           b     =     -4               b     =       3

Graph each equation on the grid below.  If the inequality has (< or >), the line

  will be a solid line.  If the inequality has (< or >), the line will be broken or open.

After graphing each line use a test point [usually (0, 0)] to determine where to

  shade in the half planes.

If the statement is true, after using the test point, shade the area of the line

  containing the point.  but if the statement is false, shade the other side of the

  line without the point.

The first graph passes through the points:  (0, -4)  &  (1, -3).  The shading is up

   and to the left.

The second graph passes through the points:  (0, 3)  &  (2, 2).  The shading is

   down and to the left.

The intersection is the part of the graph where the shading intersects.       

That is the region down and to the left of the second equation and up and to

   the left of the first equation.

_______________________________________________________________________________

Graph the system of inequalities:

                 y    >    3x    +    4         &         2y    <    3x    +    8

                 y    =    3x    +    4                     2y    =    3x    +    8

                                                                  y    =  (3/2) x    =    4

                         m    =    3/1                            m    =    3/2

                          b    =      4                               b    =      4

The first equation passes through the points:   (0, 4)  &  (1, 7).  The shading is

   up and to the left.

The second equation passes through the points:  (0, 4)  &  (2, 7(.  The shading

   is down and to the right.

The intersection of the shaded regions is in the third quadrant of the graph.

It is a little portion that is up and to the left of the first equation, and down

   and to the right of the second equation.