Five-Minute Check (over Lesson 6-7)

Main Ideas and Vocabulary

California Standards

Example 1: Solve By Graphing

Example 2: Use a System of Inequalities

• system of inequalities

• Solve systems of inequalities by graphing.

• Solve real-world problems involving systems of inequalities.

Standard 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. (Key, CAHSEE)

Solve By Graphing

A. Solve the system of inequalities by graphing.y < 2x + 2y ≥ – x – 3

Answer: The solution includes the ordered pairs in the intersection of the graphs of y < 2x + 2 and y ≥ – x – 3. The region is shaded in green. The graphs y = 2x + 2 and y = – x – 3 are boundaries of this region. The graph y = 2x + 2 is dashed and is not included in the graph of y < 2x + 2. The graph of y = – x – 3 is included in the graph of y ≥ – x – 3.

Animation: Solving Systems of Equations by Graphing

Solve By Graphing

B. Solve the system of inequalities by graphing.y ≥ –3x + 1y ≤ –3x – 2

Answer: The graphs of y = –3x + 1 and y = –3x – 2 are parallel lines. Because the two regions have no points in common, the system of inequalities has no solution.

A. A

B. B

C. C

D. D

0% 0%0%0%

A. Solve the system of inequalities by graphing 2x + y ≤ 4 and x + y > –4.

A. B.

C. D.

A. A

B. B

C. C

D. D

0% 0%0%0%

B. Solve the system of inequalities by graphing.y > 4xy < 4x – 3

A. y > 4x

B. all real numbers

C.

D. cannot be determined

SERVICE A college service organization requires that its members maintain at least a 3.0 grade point average, and volunteer at least 10 hours a week.Graph these requirements.

Words The grade point average is at least 3.0. The number of volunteer hours is at least 10 hours.

Variables If g = the grade point average and v = the number of volunteer hours, the following inequalities represent the requirements of the service organization.

Use a System of Inequalities

Inequalities The grade point average is at least 3.0.

g ≥ 3.0

Answer: The solution is the set of all ordered pairs whose graphs are in the intersection of the graphs of these inequalities.

Use a System of Inequalities

The number of volunteer hours is at least 10.

v ≥ 10

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

The senior class is sponsoring a blood drive. Anyone who wishes to give blood must be at least 17 years old and weigh at least 110 pounds. Graph these requirements.

A. B.

C. D.

http://www.ca.algebra1.com/