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Unit 5 – Systems of Equations & Inequalities: Inequalities: Sample Unit Outline TOPIC HOMEWORK DAY 1 Solving Systems of Equations by Graphing HW #1 DAY 2 Solving Systems of Equations by Substitution HW #2 DAY 3 More Practice with Graphing vs. Substitution Methods DAY 4 Quiz 5-1 DAY 5 Solving Systems of Equations by Elimination (Day 1) HW #3 DAY 6 Solving Systems of Equations by Elimination (Day 2) HW #4 DAY 7 Comparing Methods to Solving Systems HW #5 DAY 8 Word Problems HW #6 DAY 9 Quiz 5-2 None None DAY 10 Solving Systems by Matrices HW #7 DAY 11 Linear Inequalities HW #8 DAY 12 Systems of Linear Inequalities HW #9 DAY 13 Quiz 5-3 DAY 14 Systems of Linear Inequalities Word Problems HW #10 DAY 15 Review for Test; Complete Study Guide HW #11 DAY 16 UNIT 5 TEST None None See sample images of the pages on the next page. © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples SYSTEMS OF EQUATIONS The SOLUTION to a System TYPES OF SOLUTIONS Graphically: The point (x, y) where the two lines ____________________. Algebraically: The point (x, y) that makes both equations ______________. INTERSECTING LINES PARALLEL LINES SAME LINE ONE SOLUTION NO SOLUTION INFINITE SOLUTION SOLVING SYSTEMS BY GRAPHING Directions: Solve each system of equations by graphing. y = x − 8 1. y = −2 x + 1 1 y = x + 9 2. 2 y = − x + 6 y y x Solution: x Solution: © Gina Wilson (All Things Algebra®, LLC), 2012-2016 −3 x + y = 8 3. − x + y = −2 x + 2y = 4 4. 1 y = − 2 x + 2 y y x x Solution: Solution: x + 3 y = −15 5. y = −7 y = x + 5 6. x − y = 2 y y x x Solution: Solution: 3 x − 5 y = −35 7. 2 x + y = −6 x = −2 8. 3 x − 2 y = −18 y y x Solution: x Solution: © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: _________________________________ Unit 5: Systems of Equations & Inequalities Date: _______________________ Bell: ______ Homework 1: Solving Systems by Graphing ** This is a 2-page document! ** Solve each system of equations by graphing. Clearly identify your solution. 2 y = x −1 1. 3 y = − x + 4 x − y = 7 2. x − y = −4 y y x x y = x −1 3. x + 4 y = 16 5 x + 2 y = 4 4. 9 x + 2 y = 12 y y x 2 x − 6 y = 30 5. 1 y = 3 x + 1 x 5 x + 4 y = −12 6. 3 x − 4 y = −20 y x y x © Gina Wilson (All Things Algebra®, LLC), 2012-2016 x − y = 1 7. y = 5 y = −2 x − 1 8. 3 x − 4 y = −40 y y x 3 x − 2 y = −16 9. x + y = −7 x 2 x + y = 8 10. x = 5 y y x x Questions: 1) If a system of linear equations has one solution, what does this mean about the two lines? 2) If a system of linear equations has no solution, what does this mean about the two lines? 3) If a system of linear of linear equations has infinitely many solutions, what does this mean about the two lines? © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Entrance Ticket Name: _________________________________________ © Gina Wilson (All Things Algebra®, LLC), 2012-2016 1) Describe the three possible solutions to a system of equations. Solve the following systems of equations by graphing: 2) 3x + 2y = -8 x – y = -1 Entrance Ticket 3) x – 4y = 8 1 y= x+3 4 Name: _________________________________________ Solve the following systems of equations by graphing: 2) 3x + 2y = -8 x – y = -1 3) x – 4y = 8 1 y= x+3 4 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 1) Describe the three possible solutions to a system of equations. Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples Substitution Method Steps to Solve • Step 1: Solve one equation for ______ or ______. • Step 2: __________________________ this expression into the other equation and ______________ for the variable. • Step 3: ____________________ your answer into the revised equation from Step 1 and ________________ for the other variable. Examples Directions: Solve each system by substitution. y = 4x −1 1. y = 2x − 5 y = 6x 2. 2 x + 3 y = −20 y = x + 9 3. 3 x + 8 y = −5 x = 4 y + 7 4. 2 x − 6 y = 12 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 2 x + y = −2 5. 5 x + 3 y = −8 2 x − 3 y = −11 6. 2 x + y = 9 x + 5 y = 4 7. 3 x + 15 y = −1 x + 4 y = 0 8. 3 x + 2 y = 20 6 x + 3 y = 54 9. 2 x + y = 18 x − 3 y = −2 10. 10 x + 8 y = −20 3 x − y = −8 11. 5 x + 2 y = 5 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Graphing 1 y=x+6 y = -2x – 3 VS. substitution y=x+6 y = -2x – 3 2 5x – y = -5 3x – 6y = 24 5x – y = -5 3x – 6y = 24 3 2x – 3y = -12 x+y=9 2x – 3y = -12 x+y=9 4 x – 3y = -15 x = -3 x – 3y = -15 x = -3 5 y = 2x – 4 6x – 3y = 12 y = 2x – 4 6x – 3y = 12 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 6 2x + y = -8 3x – 5y = -25 2x + y = -8 3x – 5y = -25 7 2x + 9y = 27 x – 3y = -24 2x + 9y = 27 x – 3y = -24 8 x – 2y = 8 8x + 6y = 42 x – 2y = 8 8x + 6y = 42 9 2x – 2y = 14 x–y=2 2x – 2y = 14 x–y=2 10 x = 4y x + 2y = 12 x = 4y x + 2y = 12 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 I SYSTEMS OF EQUATIONS! Solve each system of equations by substitution or elimination. Partner A should do the left side and Partner B should do the right side. After each set of problems, check answers with each other. Identify your matching answers, and color the hearts accordingly. Partner A: ____________________ _________________ Partner B: ______________ ______________________ 2 x − 5 y = −22 1. x + 7 y = 27 ____________________ y = −3 x + 5 Red: 3 x − 2 y = −10 __________________ y = −3 x − 13 2. 9 x − 2 y = −4 ____________________ x + 6 y = −7 Orange: 2 x + 12 y = −14 __________________ x + y = 15 3. 4 x + 4 y = 10 ____________________ Yellow: x − 3 y = −15 4. 2x + y = 5 ____________________ 5 x − 4 y = 18 Light Green: x + y = −9 __________________ x − 2 y = −8 5. 6x + 7 y = 9 ____________________ x − 3 y = 22 Dark Green: 8 x − 6 y = 14 __________________ x + 2 y = −9 6. 5 x + 6 y = −13 ____________________ 6x − 3y = 9 Light Blue: y = 2x − 5 __________________ 3 x + y = 19 7. 4 x − 8 y = 16 ____________________ 4 x + y = 20 Dark Blue: x + 3 y = −17 __________________ x − 4 y = 31 8. x− y =4 ____________________ x − y = −5 Purple: 4x + 3y = 8 __________________ 3 x − 5 y = −12 9. y = −x − 4 ____________________ Pink: 2 x + 6 y = −28 10. x + 3 y = −14 ____________________ 5 x + 8 y = 14 White: − 3x + y = 9 1 .) HOT STUFF 6 CALL .) ME 2 .)YOU’RE MINE 7 .) YOU ROCK 3 .) TEXT ME 8 .) XOXO XOXO y = x −5 x − 7 y = −1 x + 8 y = −4 5 x + 4 y = −20 4 .) LOVE BUG 9 .)SWEET PEA __________________ __________________ __________________ 5 .) BE MINE 10 .) PUPPY LOVE © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: _________________________________ Unit 5: Systems of Equations & Inequalities Date: _______________________ Bell: ______ Homework 2: Solving Systems by Substitution ** This is a 2-page document! ** Solve each system of equations by substitution. Clearly identify your solution. y = 3 x + 19 1. y = 5 x + 33 y = −2 x + 2 2. y = 7 x + 11 y = x + 8 3. x + y = 2 y = 2x 4. 5 x − y = 9 y = x + 2 5. 3 x + 3 y = 6 x = 3y 6. 2 x + 4 y = 10 y = 2x + 1 7. 2 x − y = 3 3 x − 7 y = 41 8 x = −2 y − 21 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 5 x + 2 y = 7 9. 4 x + y = 8 x − 2y = 3 10. 4 x − 8 y = 12 2 x + y = −2 11. 5 x + 3 y = −8 2 x − 3 y = −24 12. x + 6 y = 18 8 x − y = −6 13. 2 x − 3 y = 4 x + 2 y = −2 14. 3 x + 4 y = 6 x − 3 y = 16 15. 4 x − y = 9 x − y = −10 16. 2 x + 4 y = 22 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: _____________________________________ Algebra I Date: ___________________________ Bell: ______ Unit 5: Systems of Equations & Inequalities Quiz 5-1: Solving Systems by Graphing & Substitution For questions 1 – 2, solve the system by graphing. 3 x + y = 5 y = x + 4 1. x − 4 y = 32 ANSWERS 2. x − y = 1 1. ___________ y y 2. ___________ 3. ___________ 4. ___________ x x 5. ___________ 6. ___________ For questions 3 – 6, solve the system using the substitution method. y = −2 x 3. 7 x − 8 y = −23 x − 2y = 1 5. 3 x − 6 y = 3 3 x + y = 13 4. 5 x − 2 y = 18 6 x − y = −23 6. 8 x + 3 y = −9 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples Elimination Method Steps to Solve • Step 1: Make sure the equations are lined up! • Step 2: ___________ or ___________________ the equations to eliminate the variable with common _____________________________. • Step 3: __________________ for the remaining variable. • Step 4: _______________________ your answer into either original equation and _______________ for the other variable. Examples Directions: Solve each system by elimination. y = 3x + 4 1. y = x − 2 x + 4 y = 13 2. x − y = 3 3. 3 x − 10 y = 14 3 x − 9 y = 15 4 x + 2 y = 6 4. −2 x + 2 y = 18 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 5. 4 x + 9 y = 5 −4 x + 7 y = 11 10 x − 3 y = 18 6. −2 x + 3 y = 6 x − y = 10 7. 3 x + y = 18 x = 3 y + 11 8. 2 x − 3 y = 16 4 y = 2 x − 8 9. 5 x − 4 y = 20 3 x − 4 y = −10 10. 3 x − 4 y = −13 2 x + y = −10 11. − y = 2 x + 10 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: _________________________________ Unit 5: Systems of Equations & Inequalities Date: _______________________ Bell: ______ Homework 3: Solving Systems by Elimination (Day 1) ** This is a 2-page document! ** Solve each system of equations by elimination. Clearly identify your solution. y = −x + 1 1. y = 4 x − 14 3. x − 2 y = 10 x + 3y = 5 y = −3 x + 5 2. y = −8 x + 25 2x − 3y = 9 4. −5 x − 3 y = 30 x + y = −4 5. x − y = 2 2 x − 3 y = 14 6. x + 3 y = −11 −3 x − 4 y = − 1 7. 3 x − y = −4 8. 6 x + 5 y = 4 6 x − 7 y = −20 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 3 x − 4 y = −14 9. 3 x + 2 y = −2 6 x − 3 y = 12 10. 4 x − 3 y = 24 5 x = y + 6 11. 5 x + 2 y = 3 2 x − y = −22 12. y = 7 x + 67 6 x − 3 y = −21 13. 4 x = 3 y − 9 4 y = −3 − x 14. 7 x − 4 y = 43 x + 3y = 5 15. x = −6 y + 14 −2 x − y = 12 16. y = −26 − 9 x © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples What if there are no common coefficients? EXAMPLES x + 3 y = 6 1. 2 x − 7 y = −1 9 x + 3 y = 12 2. 2 x + y = 5 3 x − y = 14 3. 5 x + 4 y = 12 x + y = −3 4. 5 x − 2 y = −50 3 x − 3 y = −3 5. 2 x − y = −5 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 3 x + y = 2 6. 6 x + 2 y = 4 3 x + 4 y = 6 7. 7 x + 8 y = 10 3 x + 3 y = 9 8. 5 x + 4 y = 10 5 x + 9 y = −10 9. 7 x + 10 y = −1 2 x = 4 y + 18 10. −5 x − 6 y = 3 2 x + 4 y = 6 11. 3 x = 12 − 6 y 7 x + 5 y = −13 12. −2 x = 7 y + 26 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: _________________________________ Unit 5: Systems of Equations & Inequalities Date: _______________________ Bell: ______ Homework 4: Solving Systems by Elimination (Day 2) ** This is a 2-page document! ** Solve each system of equations by elimination. Clearly identify your solution. x − 2 y = 12 1. 5 x + 3 y = −44 7 x − 2 y = 37 2. 4 x + y = 19 3 x + 8 y = −5 3. −2 x + 2 y = 18 x − 3y = 7 4. 2 x − 6 y = 12 2 x + y = −2 5. 5 x + 3 y = −8 2 x + 5 y = 14 6. 4 x + 2 y = −4 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 2 x − 6 y = 12 7. −5 x + 15 y = −30 5 x + 2 y = −3 8. 3 x + 3 y = 9 3 x + 2 y = −26 9. 4 x − 5 y = −4 10. 4 x + 3 y = −1 5 x + 4 y = 1 2 x + 3 y = 6 11. 2 y = 5 − x 12. 3 x = 2 y − 7 2 x − 5 y = 10 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 GROUP MEMBERS: PERIOD: _______ Comparing Methods to Solving Systems Systems of equations can be solved by graphing, substitution, or elimination. However, there are situations where one method may be more sophisticated than another. Solve the following systems using the graphing, substitution, or elimination method. You may only use each method once. SYSTEM A Method of Choice: ______ Graphing _____ Substitution _____ Elimination x − y = −2 7 x + 2 y = −5 Solution: SYSTEM B Method of Choice: ______ Graphing _____ Substitution _____ Elimination 8 x + 5 y = −13 3 x + 4 y = 10 Solution: SYSTEM C Method of Choice: ______ Graphing _____ Substitution _____ Elimination 4 x − 3 y = 18 2 x + y = 4 Solution: Answer the following question on a separate sheet of paper: What is your reasoning for picking the method for each system? © Gina Wilson (All Things Algebra®, LLC), 2012-2016 SYSTEMS OF EQUATIONS REVIEW Solve each system of equations by GRAPHING. Clearly identify your solution. x + y = 3 x + 2 y = 6 1. 2. x = 4 3 x + 2 y = 14 Solve each system of equations by SUBSTITUTION. Clearly identify your solution. y = 7x + 6 x − 7 y = −21 3. 4. − = 4 x 3 y 16 2 x − 14 y = −42 3 x − 5 y = 15 5. x − 4 y = 12 y = −5 6. 8 x + 5 y = −17 Solve each system of equations by ELIMINATION. Clearly identify your solution. x − y = −10 2 x + 2 y = 28 7. 8. 8 x − 2 y = 22 x − 6 y = −25 3 x + 6 y = 27 9. x + 2 y = 11 4 x + 5 y = 22 10. 7 x − 3 y = −32 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: _________________________________ Unit 5: Systems of Equations & Inequalities Date: _______________________ Bell: ______ Homework 5: Solving Systems – All Methods ** This is a 2-page document! ** Solve each system of equations by GRAPHING. Clearly identify your solution. 4 x − y = 3 1. 3 x + y = 4 5 x + 2 y = 4 2. 3 x + 6 y = −12 y y x x 2 x + y = 1 3. x − 2 y = 18 x − 3y = 3 4. 2 x − 6 y = −24 y y x x Solve each system of equations by SUBSTITUTION. Clearly identify your solution. x + 3y = 9 5. 4 x − 2 y = −6 2 x + 5 y = −7 6. 7 x + y = −8 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 x − 3 y = −24 7. 5 x + 8 y = −5 5 x + 3 y = 15 8. x − 6 y = 3 Solve each system of equations by ELIMINATION. Clearly identify your solution. x + y = −5 9. x − y = 9 x + 5 y = 20 10. 2 x − 7 y = −45 4 x + 3 y = −1 11. 5 x + 4 y = 1 x = 2y − 3 12. 2 x − 3 y = −5 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 SYSTEMS OF EQUATIONS Applications Many real world problems can be modeled and solved using a system of equations. Use the process below to solve these problems. 1 DEFINE YOUR TWO VARIABLES 2 WRITE A SYSTEM OF EQUATIONS using the given information. 3 4 SOLVE THE SYSTEM! ANSWER IT! Give exactly what the problem is asking for. 1. The sum of two numbers is 30 and their difference is 12. Find the two numbers. 2. The sum of two numbers is 24 and their difference is 2. What are the numbers? 3. The difference between two numbers is 9. The first number plus twice the other number is 27. Find the two numbers. 4. The sum of two numbers is 36. Twice the first number minus the second is 6. Find the numbers. 5. The sum of two numbers is 20. The difference between three times the first number and twice the second is 40. Find the two numbers. 6. The sum of two numbers is 25. One number is twice the second number plus seven. What are the two numbers? © Gina Wilson (All Things Algebra®, LLC), 2012-2016 7. The cost of 3 boxes of envelopes and 4 boxes of notebook paper is $13.25. Two boxes of envelopes and 6 boxes of notebook paper cost $17. Find the cost of each. 8. The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the cost of each. 9. Gabby and Sydney bought some pens and pencils. Gabby bought 4 pens and 5 pencils for $6.71. Sydney bought 5 pens and 3 pencils for $7.12. Find the cost of each. 10. At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43.00. Tori bought two pairs of gloves and two hats for $30.00. Find the cost of each. 11. A garden supply store sells two types of lawn mowers. The smaller mower costs $249.99 and the larger mower cost $329.99. If 30 total mowers were sold and the total sales for a given year was $8379.70, find how many of each type were sold. © Gina Wilson (All Things Algebra®, LLC), 2012-2016 12. The Town Recreation Department ordered a total of 100 baseballs and bats for the summer baseball camp. Baseballs cost $4.50 each and bats cost $20 each. The total purchase was $822. How many of each item was ordered? 13. A group of 40 children attended a baseball game on a field trip. Each child received either a hot dog or bag of popcorn. Hot dogs were $2.25 and popcorn was $1.75. If the total bill was $83.50, how many hotdogs and bags of popcorn were purchased? 14. One night a theater sold 548 movie tickets. An adult’s ticket costs $6.50 and a child’s ticket cost $3.50. In all, $2881 was taken in. How many of each kind of ticket were sold? 15. Adult tickets for the school musical sold for $3.50 and student tickets sold for $2.50. On a given night, 321 tickets were sold for $937.50. How many of each kind of ticket were sold? 16. A collection of dimes and nickels is worth $3.30. If there are 42 coins in all, how many of each kind of coin are there? © Gina Wilson (All Things Algebra®, LLC), 2012-2016 17. Mary has a collection of nickels and quarters for a total value of $4.90. If she has 42 coins total, how many of each kind are there? 18. Rob has $1.65 in nickels and dimes. He has 25 coins in all. How many of each kind of coin are there? 19. Your math teacher tells you that the next test is worth 100 points and contains 38 problems. Multiple-choice questions are worth 2 points each and word problems are worth 5 points. How many of each type of question are there? 20. Ms. Miller decides to give a test worth 90 points and contains 25 questions. Multiple-choice questions are worth 3 points and word problems are worth 4 points. How many of each type of question are there? © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Good Work! ☺ Name: ________________________________ Date: ______________________ Bell: ______ Unit 5: Systems of Equations & Inequalities Homework 6: Systems Word Problems ** This is a 2-page document! ** Solve each word problem using a system of equations. Use substitution or elimination. 1. One number added to three times another number is 24. Five times the first number added to three times the other number is 36. Find the numbers. 2. Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large cups for $2.50. If Ashley sold a total of 155 cups of lemonade for $265, how many cups of each type did she sell? 3. Your family goes to a Southern-style restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14 and some order the steak dinner for $17. If the total bill was $99, how many people ordered each dinner? 4. Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. How many adult tickets and student tickets were purchased? 5. A sporting goods store sells right-handed and left-handed baseball gloves. In one month, 12 gloves were sold for a total of $561. Right-handed gloves cost $45 each and left-handed gloves cost $52 each. How many of each type of glove were sold? © Gina Wilson (All Things Algebra®, LLC), 2012-2016 6. David bought 3 DVDs for 4 books for $40 at a yard sale. Anna bought 1 DVD and 6 books for $18. How much did each DVD and book cost? 7. Airline fares for a flight from Dallas to Austin are $30 for first class and $25 for tourist class. If a flight had 52 passengers who paid $1360, how many first class and tourist class passengers were there? 8. Sue has 100 dimes and quarters. If the total value of the coins is $21.40, how many of each kind of coin does she have? 9. At the Holiday Valley Ski Resort, skis cost $16 to rent and snowboards cost $19. If 28 people rented on a certain day and the resort brought in $478, how many skis and snowboards were rented? 10. Ben and Joel are raising money for their class trip by selling wrapping paper. Ben raised $43.50 by selling 12 rolls of solid paper and 9 rolls of printed paper. Joel raised $51.50 by selling 8 rolls of solid cost of paper and 15 rolls of printed paper. Find the cost of each type of wrapping paper. © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: _____________________________________ Algebra I Date: ___________________________ Bell: ______ Unit 5: Systems of Equations & Inequalities Quiz 5-2: Solving Systems (All Methods) – Including Word Problems For questions 1 and 2, solve the system by GRAPHING. x − y = −9 1. 3 x + 4 y = 8 ANSWERS 3 x − y = −1 2. x − 2 y = −12 y 1. ____________ y 2. ____________ 3. ____________ 4. ____________ x x 5. ____________ 6. ____________ For questions 3 and 4, solve the system using the SUBSTITUTION method. 2 x − 7 y = 13 3. 3 x + y = 8 x − 3y = 2 4. 2 x − 6 y = 6 For questions 5 and 6, solve the system using the ELIMINATION method. x + y = 3 5. x − 3 y = −29 3 y = 26 − 5 x 6. 6 x + 7 y = 21 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 For Questions 7 – 10, define the variables and set up a system of equations. Solve by substitution or elimination. Clearly give your answer. 7. Two times a number added to another number is 25. Three times the first number minus the other number is 20. Find the numbers. 8. At a baseball game, Henry bought 5 hotdogs and 3 bags of chips for $14.82. Scott bought 7 hotdogs and 6 bags of chips for $22.89. Find the cost of each hotdog and bag of chips. 9. Disney held a breakfast for parents and their children to eat with Mickey Mouse. Adult tickets cost $17.95 and children’s tickets cost $12.95. Disney made $7355 from ticket sales from a total of 500 people that attended. How many adults and how many children were at the breakfast? 10. Gabe has 60 coins consisting of quarters and dimes. The combined value of the coins is $9.45. How many quarters and dimes does Gabe have? BONUS: Create a system of equations with a solution of (-5, 2) © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples Solving Systems with Matrices Steps to Solve • Step 1: Make sure both equations are in standard form. • Step 2: Rewrite the system as a matrix and enter into your calculator. a. 2ND, x-1 b. Arrow over to EDIT, ENTER c. Enter the dimensions of the matrix as 2 x 3 d. Enter the system as a matrix • Step 3: Clear the screen by hitting 2ND, MODE • Step 4: Solve the system using calculator a. 2ND, x-1 b. Arrow over to MATH c. Select Option B: rref(, then hit ENTER d. 2ND, x-1 and choose the appropriate matrix, ENTER, ENTER Examples Directions: Solve the following systems of equations using matrices. x + y = 13 1. 2 x − 3 y = 1 x + y = 2 2. x − y = 6 9 x + 2 y = −5 3. 3 x − y = −10 2 x − 5 y = 19 4. y = 4 x − 11 −4 x − 8 y = 23 5. x + 2 y = 13 x = −6 y 6. 4 x + 7 y = −17 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 x + y = 2 7. 2 x + y = −1 8 x − 6 y = 84 8. 4 x − 42 = 3 y 2 x + 7 = 9 y 9. x = 5 y − 3 −5 x = 9 y − 20 10. 6 x + 8 y = 24 11. Two families go to a hockey game. One family purchases two adult tickets and four youth tickets for $33. Another family purchases four adult tickets and five youth tickets for $51.75. What is the cost of an adult ticket and the cost of a youth ticket? 12. Bob has 60 coins consisting of quarters and dimes. The coins combined value is $13.35. How many quarters and how many dimes does he have? 13. The next Algebra test is worth 100 points and contains 35 problems. Multiplechoice questions are worth 2 points each and word problems are 7 points each. How many of each type of equation are there? 14. On one day Fred’s Sports World sold 9 Buffalo Bills jerseys and 3 Miami Dolphin jerseys for a total of $899.40. The next day they sold 12 Bills jerseys and only 2 Dolphins jerseys for a total of $1139.30. How much is the Bills jersey and how much is the Dolphins jersey? © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: _________________________________ Date: _______________________ Bell: ______ Unit 5: Systems of Equations & Inequalities Homework 7: Solving Systems Using Matrices Solve each system of equations using matrices. Clearly give the matrix and solution. 10 x + 12 y = 6 −8 x + 2 y = −8 2. 1. 16 x 6 y 24 + = − 7 x − 3 y = −30 −20 x + 6 y = −26 3. 10 x − 3 y = 6 3 x − 5 y = −14 4. 4 x + y = 12 −4 x − 3 y = 15 5. −2 x − 6 y = 12 −2 x − 3 y = −9 6. 10 x + 6 y = −18 2 x + 6 y = −10 7. −4 x = 12 y + 20 −2 x = −6 y + 8 8. 2 y = x + 1 12 x + 30 = −9 y 9. −6 x − 26 = 10 y 3 y + 1 = 4 x 10. −10 y = 12 x − 22 11. The price of a cellular telephone plan is based on peak and nonpeak service. Kelsey used 45 peak minutes and 50 nonpeak minutes and was charged $27.75. That same month, Mitch used 70 peak minutes and 30 nonpeak minutes and was charged $36. What are the rates per minute for peak and nonpeak time? 12. Steven has a collection of nickels and dimes. In all, he has 17 coins. The total value of the collection is $1.15. How many nickels and how many dimes does he have? © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples LINEAR INEQUALITY SOLUTION to a Linear Inequality EXAMPLE Determine which ordered pairs are solutions to the linear inequality below: 2 x − 3 y < 15 (2, 5) (3, -4) (0, 0) Step 2 Step 1 Graphing linear inequalities is a way to show ALL the ordered pairs that are solutions! Steps to graph: Put the inequality in _____________- _______________________ form. Be sure to flip the inequality symbol if you multiply or divide by a negative number! Graph the line! • Use a ___________________ line for _____ or _____ symbols. • Use a ___________________ line for _____ or _____ symbols. Shade! Step 3 GRAPHING Linear Inequalities (-1,- 7) • Shade _____________ the line for _____ or _____ symbols. • Shade _____________ the line for _____ or _____ symbols. Example: 2 x − 3 y < 15 y x © Gina Wilson (All Things Algebra®, LLC), 2016 Directions: Graph each linear inequality to show all possible solutions. 2. y ≤ −2 x − 1 1 1. y > x − 5 3 3. 5 x − 2 y > 12 4. x − 4 y < 8 5. x − y ≥ 8 6. 3 x + 2 y < 0 7. y ≤ −4 8. x > 7 © Gina Wilson (All Things Algebra®, LLC), 2016 Name: _________________________________ Unit 5: Systems of Equations & Inequalities Date: _______________________ Bell: ______ Homework 8: Linear Inequalities ** This is a 2-page document! ** Graph each linear inequality to show all possible solutions. 5 1 1. y ≤ x − 4 2. y > − x + 7 y 3 2 y x x 3. 2 x + y < 1 4. 2 x − 5 y ≥ 30 y y x x 5. x − y > 5 6. 2 x − 6 y ≤ −24 y x y x © Gina Wilson (All Things Algebra®, LLC), 2012-2016 7. x − 4 y < 0 8. 2 x + 7 y ≤ −7 y y x 9. 5 x − 4 y ≥ 28 x 10. 12 x + 8 y < 24 y y x x 12. y ≤ 1 11. x > −6 y y x x © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Entrance Ticket Name: _________________________________________ Graph the following linear inequalities: “ 2) 3x – 2y ≥ 8 Identify the linear inequality shown on the graph. 3) 4) A. 2x + 5y > -5 A. 4x + y ≥ 2 B. 2x – 5y < 5 B. x + 4y ≤ 8 C. 5x + 2y > -2 C. 4x – y ≥ -2 D. 5x – 2y < 2 D. x – 4y ≤ -8 Entrance Ticket © Gina Wilson (All Things Algebra®, LLC), 2012-2016 1) y ≤ -2x + 1 Name: _________________________________________ Graph the following linear inequalities: “ 2) 3x – 2y ≥ 8 Identify the linear inequality shown on the graph. 3) A. 2x + 5y > -5 4) A. 4x + y ≥ 2 B. 2x – 5y < 5 B. x + 4y ≤ 8 C. 5x + 2y > -2 C. 4x – y ≥ -2 D. 5x – 2y < 2 D. x – 4y ≤ -8 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 1) y ≤ -2x + 1 Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples Systems of Linear Inequalities SOLUTION to a System of Linear Inequal Inequalities Directions: Graph each system of linear inequalities to show all possible solutions. y > −x − 1 1. y < x − 5 1 y < x + 7 2. 3 y ≥ − x + 4 y y x x x − 4 y ≤ 24 3. y ≤ 2x + 1 x < −4 4. 3 x + 2 y ≤ −2 y y x x 4 x − 5 y ≥ −35 5. y > −x − 2 6 x + 4 y > 12 6. 3 x − 4 y > 8 y x y x © Gina Wilson (All Things Algebra®, LLC), 2012-2016 y < −5 x + 6 7. y ≥ 2x − 1 8 y > −10 x + 24 8. y ≤ 2 y y x 3 x − y < 6 9. 3 x − y > −2 x 5 x + 2 y ≥ 4 10. x + 4 y < −8 y y x 7 x + 4 y ≥ −32 11. x − y < −3 x x − 2 y ≥ 12 12. x + 2 y ≤ −8 y y x x Application: Sarah’s Pet Store never has more than a combined total of 16 cats and dogs. She also never has more than 9 cats. Write a system of inequalities and graph to show the possible number of cats and dogs in her store. © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: __________________________________ Unit 5: Systems of Equations & Inequalities Date: _______________________ Bell: ______ Homework 9: Systems of Inequalities ** This is a 2-page document! ** Graph each system of inequalities to show all possible solutions. y > −2 x + 5 1. y ≤ x − 3 2 y ≤ − x − 3 2. 3 y ≥ 3 x + 8 5 x − 6 y > 42 3. 3 x + 2 y ≤ 14 7 x + 3 y ≤ −24 4. x + 3 y ≤ −6 x − y > 3 5. x ≥ 6 y < 2x + 5 6. 2 x − y ≤ 3 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 x + 3 y < −18 7. 5 x + 2 y ≤ 14 y ≥ −1 8. 5 x + 3 y > −18 x − 2 y < −16 9. x + y ≥ 5 x − y < −6 10. x − y ≤ 1 x − 3 y ≥ 12 11. 2 x − y ≥ −6 2 x + 5 y > 20 12. 2 x + 5 y < −5 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Entrance Ticket Name: _________________________________________ Solve the following systems of inequalities by graphing: 1. 3x + 4y < 28 2. Which of the following points are solutions to the system above? a. (1, 3) b. (3, -4) Entrance Ticket c. (0, -5) d. (-2, 0) © Gina Wilson (All Things Algebra®, LLC), 2012-2016 x – 2y ≤ 0 Name: _________________________________________ Solve the following systems of inequalities by graphing: 1. 3x + 4y < 28 2. Which of the following points are solutions to the system above? a. (1, 3) b. (3, -4) c. (0, -5) d. (-2, 0) © Gina Wilson (All Things Algebra®, LLC), 2012-2016 x – 2y ≤ 0 More with Linear Inequalities . 1) Which ordered pair is a solution to the linear inequality below? 2) Which ordered pair is a solution to the linear inequality below? x + 4y < 4 3x – 5y ≥ 10 A. (1, 4) A. (-3, 5) B. (6, -3) B. (0, 4) C. (-5, -2) C. (2, 3) D. (2, 0) D. (-8, -2) 3) Which ordered pair is a solution to the linear inequality below? 2x – 3y < 9 4) Which ordered pair is a solution to the linear inequality below? y ≥ -2x + 7 A. (6, -4) A. (-1, 5) B. (-1, -9) B. (3, 2) C. (2, -5) C. (2, -8) D. (-3, -3) D. (-4, 0) 5) Identify the ordered pairs that are solutions to the linear inequality 5x – y > 4? (-2,(4, 1)2) ( (-2,(-3, 1) 1) ( (-2,(5,1)-2) ( (-2, (2, 1) 7) ( (-2,(0,1)-1) ( (-2, (8, 1) 4) ( © Gina Wilson (All Things Algebra®, LLC), 2012-2016 6) Which ordered pair is in the solution set of the following system of inequalities? 2 x + 4 y ≤ 12 3x − y < 2 A. (-3, 2) B. (6, 4) C. (-1, -7) D. (5, -2) 7) Which ordered pair is in the solution set of the following system of inequalities? y < 2x + 2 y ≥ −x +1 A. (0, 5) B. (2, 0) C. (-1, -3) D. (-6, 4) 8) Which ordered pair is in the solution set of the following system of inequalities? 3 x + 4 y > 12 y > 2x − 1 A. (3, -5) B. (6, 0) C. (-8, -1) D. (-2, 6) 9) Which ordered pair is in the solution set of the following system of inequalities? y ≤ 3x + 1 x− y>1 A. (-1, 4) B. (4, 5) C. (-3, -6) D. (7, -2) © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: _____________________________________ Algebra I Date: ___________________________ Bell: ______ Unit 5: Systems of Equations & Inequalities Quiz 5-3: Linear Inequalities & Systems of Inequalities Graph the following linear inequalities. 1. y ≤ -2x + 1 2. 2x – 5y < 20 3. x – 3y < 0 Select the inequality that best represents the graph. 4. A. x + y ≤ -4 B. x + y ≥ -4 C. x – y ≤ 4 D. x – y ≥ 4 5. A. x < -2 B. y < -2 C. x > -2 D. y > -2 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Graph the following systems of linear inequalities. 6. x + y > 8 x>5 7. 4x + y ≥ 4 3x – 2y > 14 Use the graph to determine which ordered pair is a solution to the system of inequalities. 8. y < 2x + 1 y ≤ -3x + 4 A. (1, -4) B. (1, 5) C. (-3, 4) D. (3, 0) 9. x – 2y > -8 x+y≥1 A. (-5, 3) B. (0, 5) C. (3, -5) D. (4, 0) © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Systems of Inequalities WORD PROBLEMS 1. Suppose you buy flour and cornmeal in bulk to make flour tortillas and corn tortillas. Flour costs $1.50 per pound and cornmeal costs $2.50 per pound. You want to spend less than $25 on flour and cornmeal, but you need at least 6 pounds altogether. a. Write and graph a system of linear inequalities: ______________________________ _____________________________ b. Write two possible solutions: i. _______________ ii. _______________ 2. A seafood restaurant owner orders perch and salmon. Perch is $4/lb and salmon is $3/lb. He wants to buy at least 50 pounds of fish but cannot spend more than $240. a. Write and graph a system of linear inequalities: ______________________________ _____________________________ b. Write two possible solutions: i. _______________ ii. _______________ a. Write and graph a system of linear inequalities: ______________________________ _____________________________ b. Write two possible solutions: i. _______________ ii. _______________ © Gina Wilson (All Things Algebra®, LLC), 2012-2016 3. The “We Sell CDs” website plans to purchase ads in a local newspaper to advertise their site. Their operating budget will allow them to spend at most $3000 on this advertising adventure. An ad will cost $30 to appear in the weekday paper and $50 to appear in the weekend edition. They plan to run at least 20 ads. 4. Mary knits scarves and sweaters to sell. Scarves take 2 hours to knit and sweaters take 10 hours. Mary would like to spend no more than 40 hours per week knitting and knit at least 5 items per week. a. Write and graph a system of linear inequalities: ______________________________ _____________________________ b. Write two possible solutions: i. _______________ ii. _______________ 5. A clothing store has a going-out-of business sale. They are selling pants for $8.99 and shirts for $3.99. You can spend as much as $60 and want to buy at least two pairs of pants. a. Write and graph a system of linear inequalities: ______________________________ _____________________________ b. Write two possible solutions: i. _______________ ii. _______________ 6. You’d like to see how many baseball and soccer games you can attend this spring. Travel time for baseball games is 2 hours and soccer games is 1 hour. You would like to spend no more than 15 hours traveling to the games. In total, you would like to attend at least 8 games. ______________________________ _____________________________ c. Suppose we decide on attending 4 baseball games, what is the range of soccer games you can attend? d. Suppose we decide on attending 9 soccer games, what is the range of baseball games you can attend? e. Is it possible to attend 6 baseball games and 4 soccer games? © Gina Wilson (All Things Algebra®, LLC), 2012-2016 a. Write and graph a system of linear inequalities: Name: _________________________________ Unit 5: Systems of Equations & Inequalities Date: _______________________ Bell: ______ Homework 10: Systems by Inequalities – Word Problems ** This is a 2-page document! ** 1. Emily wants to buy turquoise stones on her trip to New Mexico to give to at least 4 of her friends. The gift shop sells small stones for $4 and large stones for $6. Emily has no more than $30 to spend. a. Write and graph a system of linear inequalities: ______________________________ _____________________________ b. Write two possible solutions: i. _______________ ii. _______________ 2. Suppose you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an hour and babysitting pays $5 an hour. You need to earn at least $60 a week. a. Write and graph a system of linear inequalities: ______________________________ _____________________________ b. Write two possible solutions: i. _______________ ii. _______________ 3. A contractor has at most $42 to spend on nails for a project. Finishing nails cost $0.45 per pound and common nails cost $0.60 per pound. He would like to purchase at least 30 pounds of nails total. a. Write and graph a system of linear inequalities: ______________________________ _____________________________ b. Write two possible solutions: i. _______________ ii. _______________ © Gina Wilson (All Things Algebra®, LLC), 2012-2016 4. A local ’theater has a maximum capacity of 1,000 people. For their latest production, adult tickets cost $25 and youth tickets cost $12.50. The theater must make at least $15,000 for the show to go on. a. Write and graph a system of linear inequalities: ______________________________ _____________________________ b. Write two possible solutions: i. _______________ ii. _______________ 5. A zoo keeper wants to fence a rectangular habitat for goats. The length of the habitat should be at least 80 feet, and the perimeter of the habitat should be more no more than 300 feet. a. Write and graph a system of linear inequalities: ______________________________ _____________________________ b. Write two possible solutions: i. _______________ ii. _______________ © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Unit 5 Test Study Guide Name: _________________________________________ (Systems of Equations & Inequalities) Date: ____________________________ Per: __________ Topic 1: Solving Systems of Equations by Graphing Solve each system of equations by graphing. x + y = 2 1. x − y = 4 3 x − 5 y = 15 2. y = 2x + 4 y y x x x − 4 y = 28 3. x + 2 y = −2 3 y = 4 x − 6 4. 8 x − 6 y = −30 y x y x Topic 2: Solving Systems of Equations by Substitution Solve each system of equations by substitution. y = 2x + 3 5. y = −x − 9 2 x + 3 y = 4 6. y = 5 x − 27 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 x + 4 y = 19 7. x − 2y = 1 6 x − y = −21 8. 5 x + 3 y = 17 Topic 3: Solving Systems of Equations by Elimination Solve each system of equations by elimination. x − 3 y = −13 9. 3 x + 7 y = 25 2 x + 8 y = 6 10. 5 x + 20 y = 15 7 x − y = 19 11. 2 x − 3 y = 19 4 x − y = −4 12. 5 x = 2 y + 1 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Topic 4: Systems of Equations Applications Define variables, set up a system of equations, then solve by substitution elimination. 13. A tennis coach took his team out for lunch and bought 8 hamburgers and 5 fries for $24. The players were still hungry so the coach bought 6 more hamburgers and 2 more fries for $16.60. Find the cost for one hamburger. 14. Jim sells hot dogs for $2.95 each and steak sandwiches for $9.95 each out of his food cart. During a busy outdoor festival, he sold a total of 985 items for $7343.75. How many steak sandwiches did he sell? 15. Bob bought 24 hockey tickets for $83. Adult tickets cost $5.50 and child tickets cost $2.00. How many child tickets did he buy? 16. Ethan makes $6 per hour mowing lawns and $7.50 per hour bagging groceries. Last week, he made a total of $129. The difference between the number of hours bagging groceries and the number of hours mowing lawns was 10. How many hours did Ethan spend mowing lawns? 17. Dustin has only nickels and quarters in his piggy bank. He has 49 coins total for a combined value of $8.85. How many of each type of coin does he have? © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Topic 5: Linear Inequalities Graph each linear inequality to show all possible solutions. y 18. 2 x − 3 y < 6 19. x ≥ −3 y x x Topic 6: Systems of Linear Inequalities Graph each system of linear inequalities to show all possible solutions. y < 3x − 2 20. y > −x + 3 y 2 x − y ≥ 0 21. 3 x + y < 5 x y x Topic 7: Systems of Linear Inequalities Application 22. Rob works part time at the Fallbrook Riding Stable. He makes $5 an hour exercising horses and $10 an hour cleaning stalls. Because Rob is a full-time student, he can work no more than 12 hours per week. However, he must make at least $60 per week. a. Write and graph a system of inequalities: _________________________________ _________________________________ b. Write two possible solutions: i. __________________________________ ii. __________________________________ © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: _________________________________ Unit 5: Systems of Equations & Inequalities Date: _______________________ Bell: ______ Homework 11: Unit 5 Review ** This is a 2-page document! ** Solve each system of equations by graphing. Clearly give your solution. 2. -4x – 2y = -8 1. 3x + y = 5 y y = 2x + 4 -x – y = 1 y x x Solve each system of equations by substitution. Clearly give your solution. 3. 2x + 5y = -7 4. x – 3y = -24 7x + y = -8 5x + 8y = -5 Solve each system of equations by elimination. Clearly give your solution. 5. x + 2y = 3 6. 2x = 8y – 2 5x + 3y = 8 3x – 3y = 15 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 7. Karen and Holly took their families out to the movie theater. Karen bought three boxes of candy and two small bags of popcorn and paid $18.35. Holly bought four boxes of candy and three small bags of popcorn and paid $26.05. Find the cost for a box of candy. 8. Mr. Delaney broke his piggy bank with a sledge hammer and found that it only contained quarters and pennies. If he had a total of 120 coins for a combined value of $16.32, how many pennies did he have in his piggy bank? Graph the following linear inequalities. 9. 2x – 4y < 8 10. y ≥ -3 y y x x Graph the following systems of linear inequalities. 11. y < 2x – 3 12. x – y ≥ 0 4x + 3y < 18 y > -x + 1 y x y x © Gina Wilson (All Things Algebra®, LLC), 2012-2016 Name: _________________________________________ Date: _______________________________ Bell: ______ Algebra I Unit 5 Test (Systems of Equations & Inequalities) SHOW ALL WORK NEEDED TO ANSWER EACH QUESTION! PLACE YOUR FINAL ANSWER IN THE BOX. GOOD LUCK! ☺ For questions 1 and 2, solve the system of equations by GRAPHING. x + y = 4 1. 2 x − 5 y = 15 y y y = −2 x + 3 2. 8 x + 4 y = 12 x x For questions 3 and 4, solve the system of equations by SUBSTITUTION. 6 x + 2 y = −26 3. x − 6 y = 21 5 x + y = −10 4. 4 x − 7 y = −8 For questions 5-8, solve the system of equations by ELIMINATION. x + 2 y = −14 5. x − y = 13 2 x − 3 y = 23 6. x + 3 y = −20 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 2 x − y = 11 7. 6 x − 3 y = 15 7 x = 3 y + 45 8. 4 x + 5 y = 19 For questions 9-11, define variables, set up a system, then solve by substitution or elimination. 9. Erin bought 4 jars of jelly and 6 jars of peanut butter for $19.32. Adam bought 3 jars of jelly and 5 jars of peanut butter for $15.67. Find the cost of a jar of peanut butter. 10. Karen makes $5 per hour babysitting and $12 per hour giving music lessons. One weekend, she worked a total of 18 hours and made $139. How many hours did she spend babysitting? 11. Carter has 37 coins, all nickels and dimes in his piggy bank. The value of the coins is $3.10. How many dimes does Carter have? © Gina Wilson (All Things Algebra®, LLC), 2012-2016 12. Which graph represents the solution to the inequality 2x – y ≥ -3? C. B. A. 13. Which inequality is shown on the graph? D. 14. In the graph of y ≤ x, which quadrant is completely shaded? Use the graph below to determine. A. x < 3 A. Quadrant I B. x > 3 B. Quadrant II C. y < 3 C. Quadrant III D. y > 3 D. Quadrant IV 15. Which ordered pair is a solution to the linear inequality given below? Use the graph to determine. y 3 x + 4 y ≥ 20 A. (-5, 1) B. (0, -3) x C. (-4, -2) D. (2, 7) y ≤ 2x + 1 16. Which graph represents the solution to the following system of inequalities? 2 x − 5 y ≤ 10 A. B. C. D. © Gina Wilson (All Things Algebra®, LLC), 2012-2016 17. Which ordered pair is NOT in the solution set to the following system of inequalities? Use the graph to determine. y 3 x + y > −3 x + 2y < 4 A. (1, 1) B. (-1, 2) x C. (4, -3) D. (-5, 1) 18. In order to save money for prom this weekend, Tom is going to walk his neighbor’s dog for $6 per hour and wash cars for $7.50 per hour. His mother told him he can work no more than 15 hours in order to keep up with his homework. If Tom would like to make at least $75 to cover prom expenses, help him determine combinations of hours he can work between these two jobs. a. Write and graph a system of inequalities. _________________________________ _________________________________ b. Write two possible solutions: i. _________________________________ ii. _________________________________ BONUS: Solve the following system by substitution or elimination. 14 2 3 x + y = 3 4 x − 3 y = −10 5 4 © Gina Wilson (All Things Algebra®, LLC), 2012-2016 I use clipart and fonts in my products by: Art with Jenny K Many thanks to these talented artists!