Practice with
Systems of Inequalities
 Topic Index | Algebra Index | Regents Exam Prep Center




For the first four questions, you will need paper and pencil for graphing.  If you have graph paper, please use your graph paper.  Use your graphing calculator for checking.

1.

Solve the following system of inequalities graphically:

x + 2y 8

y x + 4

 
Click for Answer



 

2.

Solve the following system of inequalities graphically:

y 1

y 2x -3

  


Click for Answer

 

 

3.

Solve the following system of inequalities graphically:

x + y > 2

y x 

 
Click for Answer

 

 

4.

Solve the following system of inequalities graphically:

y > -3

y > x + 1

  


Click for Answer



 

5.

In 1958, NASA began its search for astronauts for project Mercury, the first man-in-space program.  The initial qualifications for astronaut candidates specified males between 25 and 40 years of age, who were at least 5-foot, 4 inches tall but no taller than 5 foot, 11-inches.   Write and graph a system of inequalities that represent the range of heights and ages for qualifying astronauts.


                                                    Photo courtesy of NASA
Project Mercury Astronauts:  Left to right: Scott Carpenter,
Gordon Cooper, John Glenn, Gus Grissom, Walter Schirra,
 Alan Shepard, and Deke Slayton.
 

 


 

6. Katie works part-time at the Fallbrook Riding Stable.  She makes $5 an hour for exercising horses and $10 an hour for cleaning stalls.   Because Katie is a full-time student, she cannot work more than 12 hours per week.  Graph two inequalities that illustrate how many hours Katie needs to work at each job if she plans to earn not less than $90 per week.