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Linear Non Linear Systems of Equations

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Linear Non Linear Systems of Equations Powered By Docstoc
					Linear & Non-Linear Systems of
          Equations
  Graphing Linear Inequalities in
         Two Variables
         Learner Outcome 1.1
                 The Boundary Line

                                             y=x
All the points on the
line of y = x, satisfy
the equation y = x.
                                               (5, 5)




                                    (0, 0)

                                        The boundary line divides
                         (-5, -5)       the coordinate plane into
                                        two regions.
                    The Region ABOVE
For every point in the region
above the boundary line, y > x.         y=x
                 (-10, 7)

                              (-5, 5)
     (-15, 4)


                   (-10, 1)



       (-15, -3)

                (-12, -5)
The Region BELOW
                                      (14, 7)


                           (10, 4)




            (2, -2)

                           (10, -5)
             For every point in
 (-7, -8)    the region below the
             boundary line, y < x.
              The Boundary Line
• The boundary line for an inequality may be
  solid or broken.



                                                 Broken Line
                   Solid Line




   y>x+3                        y>x+3
   y = x + 3 is part            y = x + 3 is not part
   of the solution.             of the solution.
                Shading
• If you have y > or ≥, you shade ABOVE
• If you have y < or ≤, you shade BELOW

Example:
• Graph: - 4x + 3y > 12
• Use a test point to check if you shaded
  the appropriate region.
Word Problems

Example:
The library staff wants to plant flowers on the boulevard.
   During a sale at the greenhouse, a flat of marigolds costs $5
   and a flat of petunias costs $6, including tax. The library
   staff can spend a maximum of $60.
a. Write an inequality to describe the numbers of flats of
    marigolds and flats of petunias they can buy.
b. What are the restrictions on the variables?
c. Graph the inequality.
d. Use the graph to find four possible combinations of flats of
    marigolds and petunias the staff could buy (assume only
    whole flats can be bought).
   HOMEWORK:
        Page 75
#2-34 even, 35-37, 41-45

				
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posted:6/11/2012
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