Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Determine whether the ordered pair is a solution of the given system.

7. (2, 12);

   y > 2 x + 4 y greater than 2 x plus 4

   y < 3 x + 7 y less than 3 x plus 7

8. (8, 2);

   3 x − y ≤ 17 3 x minus y less than or equal to 17

   0.3 x + 4 y > 9 0.3 x plus 4 y greater than 9

9. ( − 3 , 17 ) ; open negative 3 comma 17 close semicolon

   y > − 5 x + 2 y greater than , minus 5 , x plus 2

   y ≥ − 3 x + 7 y greater than or equal to , minus 3 , x plus 7

Solve each system of inequalities by graphing.

10. y < 2 x + 4 y less than 2 x plus 4

    − 3 x − 2 y ≥ 6 negative 3 x minus 2 , y greater than or equal to 6

11. y < 2 x + 4 y less than 2 x plus 4

    2 x − y ≤ 4 2 x minus y less than or equal to 4

12. y > 2 x + 4 y greater than 2 x plus 4

    2 x − y ≤ 4 2 x minus y less than or equal to 4

13. y > 1 4 x y greater than , 1 fourth , x

    y ≤ − x + 4 y less than or equal to negative x plus 4

14. y < 2 x − 3 y less than 2 x minus 3

    y > 5 y greater than 5

15. y ≤ − 1 3 x + 7 y less than or equal to negative , 1 third , x plus 7

    y ≥ − x + 1 y greater than or equal to negative x plus 1

16. x + 2 y ≤ 10 x plus 2 y less than or equal to 10

    x + 2 y ≥ 9 x plus 2 . y greater than or equal to 9

17. y ≥ − x + 5 y greater than or equal to negative x plus 5

    y ≤ 3 x − 4 y less than or equal to 3 x minus 4

18. y ≤ 0.75 x − 2 y less than or equal to , 0.75 , x minus 2

    y > 0.75 x − 3 y greater than , 0.75 , x minus 3

19. 8 x + 4 y ≥ 10 8 x plus 4 . y greater than or equal to 10

    3 x − 6 y > 12 3 x minus 6 y greater than 12

20. 2 x − 1 4 y < 1 2 x minus , 1 fourth . y less than 1

    4 x + 8 y > 4 4 x plus 8 y greater than 4

21. 6 x − 5 y < 15 6 x minus 5 y less than 15

    x + 2 y ≥ 7 x plus 2 . y greater than or equal to 7

See Problem 2.

Write a system of inequalities for each graph.

22. 
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    See Problem 3.

26. Earnings Suppose you have a job mowing lawns that pays $12 per hour. You also have a job at a clothing store that pays $10 per hour. You need to earn at least $350 per week, but you can work no more than 35 h per week. You must work a minimum of 10 h per week at the clothing store. What is a graph showing how many hours per week you can work at each job?
27. Driving Two friends agree to split the driving on a road trip from Philadelphia, Pennsylvania, to Denver, Colorado. One friend drives at an average speed of 60 mi/h. The other friend drives at an average speed of 55 mi/h. They want to drive at least 500 mi per day. They plan to spend no more than 10 h driving each day. The friend who drives slower wants to drive fewer hours. What is a graph showing how they can split the driving each day?

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