Algebra 1 Honors Unit 5 Study Guide (2024) PDF

Name ___________________ Date ___________ Period ___ UNIT 5 STUDY GUIDE Algebra 1 Honors Systems of Equations & Inequalities Question 3 : Directions: Solve a...

Name ___________________ Date ___________ Period ___ UNIT 5 STUDY GUIDE Algebra 1 Honors Systems of Equations & Inequalities Question 3 : Directions: Solve all problems algebraically on your work page and then submit your answers Use the SUBSTITUTION in Formative to check your work. You may METHOD to find the solution to the following resubmit answers to earn 100% prior to the system of equations. test date. This will help you to prepare for the Unit 5 Test. On both this study guide and the Unit 5 Test, you may use a scientific calculator, but not a graphing calculator. Question 1 : This is a graph of a system of equations. Which is most likely the solution to the system of equations shown? _____________ Question 4 : Solve the system of equations using the ELIMINATION METHOD. Write your Question 2 : answer as an ordered pair. Plot to find the solution to the system -6x + 6y = 30 of equations on the graph. -2x - 5y= -18 y=-6 3x – 3y = 9 _______________ UNIT 5 STUDY GUIDE Systems of Equations & Inequalities Question 5 : Question 7: Solve the System of equations using either Solve the System of equations using the the Substitution or Elimination method. Graphing Method. x− y =4 2x − y = 2 Question 8 : Solve the System of equations using either the Substitution or Elimination method. 𝟏 𝟔 𝒙+𝒚 = Question 6 : {𝟓 𝟏𝟎 𝟏 𝟏 𝟓 𝒙+ 𝒚= Solve the System of equations using either 𝟏𝟎 𝟑 𝟔 the Substitution or Elimination method. -3x + y = -8 -7x – y = -22 UNIT 5 STUDY GUIDE Systems of Equations & Inequalities Question 11 : Question 9 : Write and solve a system of equations. Be sure to define your variables first. Solve the System of equations using either the Substitution or Elimination method. The perimeter of a rectangle is 40 inches. The Determine weather there is one solution, length is two inches more than three times the no solutions, or infinite solutions. width. Find the dimensions of the rectangle. Question 10: Question 12 : Identify the number of solutions of each system Write and solve a system of equations. Be sure to of equations. define your variables first. The difference in cost between a large bag of chips and a small bag of chips was $0.90. Alicia bought 5 large bags and 3 small bags of chips for her party and spent $17.22. What was the cost of a small bag of chips? Answer choices: Infinitely many solutions Two solutions One solution No solution UNIT 5 STUDY GUIDE Systems of Equations & Inequalities Question 13: Question 15 : Write and solve a system of equations. Be sure to define your variables first. You need to order 13 pizzas for a class party. Cheese pizzas cost $7.50 each and The next algebra test is worth 100 points and pepperoni pizzas cost $8.50 each. The cost of contains 35 problems. Multiple choice problems the pizzas was $101.50. Write and solve system are worth two points each and word problems are of equations to determine the number of worth seven points each. If the amount of cheese pizzas, , and pepperoni pizzas, , multiple-choice problems is seven less than six purchased? times the number of word problems, how many of each type of problem is there? Question 16 : Question 14 : Write and solve a system of equations. Be sure to define Graph the inequality your variables first. Three pairs of jeans and six shirts cost $104.25. The cost of 4 pairs of jeans and 5 shirts is $112.15. Find the cost of each pair of jeans and each shirt. UNIT 5 STUDY GUIDE Systems of Equations & Inequalities Question 17 : Question 19 : Write the inequality of the graph shown below: Graph the following system of inequalities. Then identify all solution(s) to the system of linear 𝒚 ≥ 𝟐𝒙 − 𝟒 inequalities: { 𝟑𝒙 + 𝟒𝒚 < 𝟏𝟔 A: (-6,-4) B: (4, -1) C: (0, 4) D: (-2,8) _____________________________ E: (2, 0) F: (-4,3) Question 18: Write and solve a system of inequalities. Be sure to define your variables first. Mary knits scarves and sweater 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 Question 20 : knit at least 5 items per week. Identify the system of inequalities represented by the graph. Sweaters 𝐿1 ________________________ Scarves 𝐿2 _______________________ UNIT 5 STUDY GUIDE Systems of Equations & Inequalities Question 21 : Question 23: Solve and graph the following problem by using a Solve the system of linear inequalities by system of inequalities. Write your answer as a graphing and shading your solution: short sentence. 𝟐 𝒚≤− 𝒙−𝟑 You plan to buy flour and cornmeal in 𝟑 order to make flour tortillas and corn 𝒚 > 𝟑𝒙 + 𝟖 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. Cornmeal Flour Question 24: Circle the point(s) that are part of the solution set. Question 22 : Determine whether the ordered pair is solution to the given system of inequalities: 𝒚 ≥ −𝒙 − 𝟖 (5, -4) 𝒚 < −𝟐𝒙 + 𝟔 (-1, 3) (2, -1) (-2, -4) (4, -2) (3, -3) (6, -5) (2, -3) (3, -5)