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Graph the linear inequality

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					Alg_Problem Set 7-16 (Chapter 7 Review #3)                                              Name _____________________________

Graph the Systems of Linear Inequalities.

       y  2x  4                                              y  2x  4                                  y  2x  3
  1)                                                 2)                                              3)
        3x  2 y  6                                          2x  y  4                                  y5

                             y                                                  y                                                      y
                         6                                                  6                                                      6


                         4                                                  4                                                      4


                         2                                                  2                                                      2



  –6   –4       –2                2    4    6   x         –6     –4   –2            2    4   6   x        –6   –4        –2                 2        4       6       x

                     –2                                                    –2                                                 –2


                     –4                                                    –4                                                 –4


                     –6                                                    –6                                                 –6


Write a System of Linear Inequalities shown in each graph.

4) ___________________                               5) ____________________                          6) ______________________

   ___________________                                    ____________________                             ______________________
                             y                                                  y                                                                y
                         6                                                  6                                                                6


                         4                                                  4                                                                4


                         2                                                  2                                                                2



  –6   –4       –2                2    4    6   x         –6     –4   –2            2    4   6   x                  –6        –4       –2                2       4       6   x

                     –2                                                    –2                                                               –2


                     –4                                                    –4                                                               –4


                     –6                                                    –6                                                               –6




7) You can work at most 20 hours per week. You need to earn at least $90 to cover your weekly expenses. Your
dog-walking job pays $9 per hour and your job as a car wash attendant pays $10 per hour. Write a system of
linear inequalities to model the situation and graph.
       HrsDog

  24

  20

  16

  12

   8

   4


            4        8       12   16   20   HrsCar
Alg_Problem Set 7-16 (Chapter 7 Review #3)                  Name _____________________________


8) The available parking area of a parking lot is 600 square meters. A car requires 6 square meters of space and
a bus requires 30 square meters of space. The attendant can handle no more than 60 vehicles. Write a system of
inequalities to represent the amount of space available and the total number of vehicles allowed. Graph the
system.

        #Cars

  120

  100

  80

  60

  40

  20


          20     40   60   80 100   #Buses

9) Mary is selling bracelets and earrings to make money for spring break. The bracelets cost $2 and earrings cost
$3. She needs to make at least $450 and knows that she will sell more than 50 bracelets. Write a system of linear
inequalities and graph the inequalities.
        # Ear.

  300

  250

  200

  150

  100

  50


          50 100 150 200 250         # Br.



10) A club is selling hats and jackets as a fundraiser. They have to stay within a budget of $900. They can order
up to 200 items. They must buy at least as many hats as they buy jackets. Each hat costs $3 and each ribbon costs
$4.




11) How many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 30%
alcohol solution?
Alg_Problem Set 7-16 (Chapter 7 Review #3)                       Name _____________________________

                                                 x  y  10
                                                 3x  4 y  24
12) Graph the system of linear inequalities.
                                                 x0
                                                 y0

   12

   10

    8

    6

    4

    2


           2      4    6    8   10   12


============================================================================
EXTRA PRACTICE PROBLEMS

EP1) A farmer has 90 acres available for planting millet and alfalfa. Seed costs $4 per acre for millet and $6 per
acre for alfalfa. Labor costs are $20 per acre for millet and $10 per acre for alfalfa. The expected income is $110
per acre for millet and $150 per acre for alfalfa. The farmer intends to spend no more than $480 for seed and
$1400 for labor. Set up a system of linear inequalities and graph.

        Alfalfa

  120

  100

   80

   60

   40

   20


           20     40   60   80 100    Millet




EP2) Write a system of linear inequalities that defines a triangle with vertices at (0, 0), (–5, 0) and (–2, 5).
Alg_Problem Set 7-16 (Chapter 7 Review #3)                                             Name _____________________________

====================================================================================
ANSWERS
1)                                                      2)                                                      3)
                             y                                                    y                                                        y
                         6
                                                                                                                                       6

                         4                                                   4
                                                                                                                                       4


                         2                                                   2                                                         2



                                                                  –4   –2               2        4         x          –6   –4    –2            2   4   6   x
 –6     –4     –2                2    4       6 x
                                                                            –2                                                        –2
                        –2

                                                                                                                                      –4
                        –4                                                  –4

                                                                                                                                      –6
                        –6




                                                             1
                                                             yx 1
      y3                                                    3                                            x  1
4)                                                      5)                                       6)
      y  4x  1                                             4                                            y  3x  3
                                                           y x2
                                                             3

7) c = # hours at car wash                                                             8) b = # busses
   d = # hours dog walking                                                                c = # cars
   c  d  20                                                                             30b  6c  600
   10c  9d  90                                                                          b  c  60
             Dog ( H)
        20
                                                                                        #Cars
        18
        16                                                                       120
        14
        12                                                                       100
        10
                                                                                 80
         8
         6
                                                                                 60
         4
         2                                                                       40

              2     4    6   8 10 12 14 16   Car ( H)                            20


                                                                                            20       40    60        80 100     #Buses
Alg_Problem Set 7-16 (Chapter 7 Review #3)         Name _____________________________



9) b = # bracelets                                 10) h = # hats
   e = # earrings                                      j = # jackets
                                                        h  j  200
      b  50
                                                       3h  4 j  900
      2b  3e  450
                                                       h j

                # Ear.                                     #Jack.

          300                                        300

          250                                        250

          200                                        200

          150                                        150

          100                                        100

          50                                          50


                  50 100 150 200 250       # Br.             50 100 150 200 250   #Hats




11) a = # gallons of 20%
    b = # gallons of 50%
    a+b=9
   .2a + .5b = 9(.3)
   6 gallons of 20%
   3 gallons of 50%


12)

  12

  10

      8

      6

      4

      2


            2     4      6   8   10   12
Alg_Problem Set 7-16 (Chapter 7 Review #3)                Name _____________________________

                                                         y0
                                                           5    25
EP1) m = # acres of millet planted                  EP2) y  x
                                                           3    3
                                                             5
                                                         y x
                                                             2
      a = # acres of alfalfa planted
      m  a  90
      4m  6a  480
      20 m  10 a  1400
              Alfalfa

        120

        100

         80

         60

         40

         20


                 20     40   60   80 100   Millet

				
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