Algebra 2 Companion Book, Volume 1

3.1.3 Solving Systems of Linear Inequalities - Worksheet

Example 1: Graph each system of inequalities. 1. 2.

3.

4.

  

  

x y y x 7

x y x y

  

  

y x y x

+ ≤ − > x y x y 2 2 4 3 1

16 5 2

+ > − <− 5

4 4 3 3

< − ≤− −

≥ − ≥ −

3

Example 2: 5.  A charity is selling T-shirts in order to raise money. The cost of a T-shirt is $15 for adults and $10 for students. The charity needs to raise at least $3000 and has only 250 T-shirts. Write and graph a system of inequalities that can be used to determine the number of adult and student T-shirts the charity must sell. Example 3: Graph the system of inequalities and classify the figure created by the solution region. 6. ≥ ≥− ≤ ≤−  x y x y 9 18 13 4 7. ≤ x y x y 7 2 − ≤ + ≥−      y 3 2 6 8. ≤− ≤ + ≥− − 3 2      x y x y x 1 3 10 9. ≥ ≤ + ≤ ≥− 6 2        y x y x x x 6      

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