Algebra 2

Unit 7B: Linear Systems

Learning Targets6. I can solve a system of inequalities

Day Date Topic Assignment

1Monday4/25/16

Systems of Linear Inequalities ALEKS

2Tuesday4/26/16

Systems of Linear Inequalities Assignment #31

3Wednesday4/27/16

Systems of Linear Inequalities Assignment #32

4Thursday4/28/16

Unit 7B Test

Algebra 2Assignment #31Unit 7B: Linear Systems

Name:

Period:

Solve each system of inequalities by graphing.1. { x+ y ≥22x+ y ≤5

2. { y>xy<x+1

3. {y≥−3 x−1y<x+24. {y>−2

x<1

5. { y ≤3 x+1−6 x+2 y>5

6. {x+2 y ≤10x+ y ≤3

7. You spend no more than 3 hours each day watching TV and playing football. You play football for at least 1 hour each day. What are the possible numbers of hours you can spend on each activity in one day?

8. Describe and correct the error made in solving this system of inequalities.

{ y< 12 x−1y≤−3 x+3

Solve each system of inequalities by graphing.

10. 11. 12.

1. An ice cream parlor charges $0.25 for each sauce topping and $0.50 for each candy topping. You want at least 5 toppings on your ice cream. You have $6 to spend on toppings. Write a system of linear inequalities to model this scenario.

Jim works at Six Flags for $8 per hour. He also works at a day camp for $7 per hour. He is only allowed to work 25 hours per week. He wants to make at least $125.

2. Write a system of linear inequalities to represent this situation.

3. Graph the system of inequalities.

1. The solution to a system of linear equations is a(n) ______________________________________________

that makes all of the equations ____________________________.

2. How many solutions can system of two linear equations have?

Solve each system of equations by using a table.3. { y=3 x−4y=−2 x+11

4. { 4 x− y=15x+2 y=24

A museum charges $8.50 for adult tickets and $5.25 for children’s tickets. On Friday they made $650.

5. Write an equation that can be used to model the ticket sales.

6. Graph the equation.

Graph each equation.7. 3 x+5 y=15 8. y=−x+6

Algebra 2Assignment #23Unit 7A: Linear Systems

Name:

Period:

Solve each system of equations by graphing.1. { y=x−1y=−x+3

2. {2x+ y=4x− y=2

3. { y=−x+3

y=32x−2

4. {x=−3y=5

5. {3x+ y=5x− y=76. {−3 x+2 y=8x+4 y=−12

Write and solve a system of equations for each situation. Check your answers.

7. You buy a total of 6 pens and pencils for $4. If each pen costs $1 and each pencil cost $.50, how many pens did you buy? How many pencils?

8. A store sells small notebooks for $8 and large notebooks for $10. If you buy 6 notebooks and spend $56, how many of each size notebook did you buy?

9. A shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50. If you buy 5 bags and spend $17, how many of each size bag did you buy?

Without graphing, does each system have zero, one, or infinitely many solutions?10. {−3 x+ y=4x−1

3y=1

11. { 7x− y=6−7 x+ y=−6

12. {4 x+8 y=12x+2 y=−313. { y=2 x−1y=−2 x+5

Algebra 2Assignment #24Unit 7A: Linear Systems

Name:

Period:

Solve each system of equations by substitution.1. {3x+5 y=13y=−2x+4

2. {2x−3 y=6y=−x−12

3. {4 x+2 y=7y=5 x4. {3c+d=2d=4

5. {4 p+2q=8q=2 p+16. { x=−3 y+7

2x−4 y=24

7. { x+6 y=25x+4 y=368. { y=2 x−13x− y=−1

Without graphing, does each system have zero, one, or infinitely many solutions?9. { x=6y=−2

10. { x−3 y=24 x−12 y=8

Solve each system of equations by graphing.11. {2x+4 y=12x+ y=2

12. {2x−2 y=4y−x=6

Your cell phone company offers two text-messaging plans. One plan costs $.25 per text message, plus a monthly fee of $9. The other plan costs $.40 per text message with no monthly fee.

13. For how many text messages will both plans cost the same amount?

14. If you use about 80 text message each month, which plan should you choose? Explain.

Algebra 2Assignment #25Unit 7A: Linear Systems

Name:

Period:

Solve each system using elimination.1. { 2x+3 y=7−2x+5 y=1

2. { x− y=−43x+2 y=7

3. {3x+4 y=102 x+3 y=74. {x+2 y=−1

x− y=8

5. {x+ y=12x− y=26. {x+2 y=10x+ y=6

7. { 3 a+4 b=9−3a−2b=−3

8. {4 x+2 y=46 x+2 y=8

9. { 3u+3v=15−2u+3v=−510. {5x− y=42 x− y=1

11. {4 x−6 y=−26−2x+3 y=13

12. { 9a−3b=3−3a+b=−1

13. Suppose you have a part-time job delivering packages. Your employer pays you a flat rate of $9.50 per hour. You discover that a competitor pays employees $2 per hour plus $3 per delivery. How many deliveries would the competitor’s empoyees have to make in four hours to ear the same pay you earn in a four-hour shift?

14. A scientist wants to make 6 milliliters of a 30% sulfuric acid solution. The solution is to be made from a combination of a 20% sulfuric acid solution and a 50% sulfuric acid solution. How many milliliters of each solution must be combined to make the 30% solution?

Algebra 2Assignment #25Unit 7A: Linear Systems

Name:

Period:

Number of Solutions, what the graphs look like, without graphing- No solution- One solution- Infinitely many solutions

Create a system of equations with a specific number of solutions

What is a solution to a system of equations?

Identify the graph of a system of equations

Write a system of equations to represent a situation

Identify what the variables in a system represent

Solve a system of equations algebraically

Solve a system of equations graphically

Solve a system of inequalities graphically

Where is the solution to a system of inequalities?

Number of solutions to a system of inequalities

Solve each system of equations by graphing.

1. 2. 3.

Solve each system of equations.

4. 5. 6.

Without solving, identify the number of solutions for each system of equations.

7. 8. 9.

10.You and your friend are both reading the same book. You read 50 pages each hour and already have read 10 pages. Your friend reads 30 pages each hour and has already read 25 pages. To determine when you will both have read the same number of pages, write a system of equations.

An online movie company offers 60 downloads for $25.00 and 40 downloads for $20.00. Each price includes the same one time registration fee.

11.Write a system of equations to represent this situation.

12.What do your variables represent?

13.Solve the system.

14.A student has some nickels and quarters in his pocket. . He has a total of 38 coins that are worth $7.50. How many of each type of coin did he have?