REVIEW elimination method parallel rational numbers Vocabulary BLOCK 4 solution to a system of linear equations substitution method system of linear equations Lesson 4. ~ Parallel, Intersecting or The Same Line Determine if each graph shows a system of linear equations that is intersecting, parallel or the same line. State how many solutions there are for each system... 3. Algebraically determine if the two lines in each system of equations are intersecting, parallel or the same line. State how many solutions there will be for each system. Use words and/or numbers to show how you determined your answer. 4. y = _ x 4 5. 3x + 4y = 6. 6x + 3y = y = _ x + 4 y = 3_ 4x y = (x + ) + Lesson 4. ~ Solving Systems by Graphing Decide whether the given ordered pair is a solution of the system of equations. Show all work necessary to justify your answer. 7. y = x 8. x 3y = 4 9. y = x y = _ 3 x + 4 4x + y = 5 4x + y = (3, 5) (, ) (, ) Block 4 ~ Review 75
Solve each system of equations by graphing. Show all work necessary to prove that your answer is correct.. y = _ x 3. y = x 4. y = _ 3 x y = x 5 y = _ x + y = 3. Sandra and Terry each walk to the same school from different neighborhoods. They do not cross paths until they reach the school building. Sandra follows the path represented by the equation y = x + and Terry follows the path represented by the equation y = _ 6 x. What are the coordinates of the school building? Lesson 4.3 ~ Solving Systems Using Tables Solve each system of equations using the given input-output tables. Show all work necessary to prove that your answer is correct. 4. y = 5x 4 3 y = x + 3 3 5. y = 5 + x 5 4 3 y = 3x + 3 5 4 3 Solve each system of equations using input-output tables. Show all work necessary to prove that your answer is correct. 6. y = 3x 4 7. y = 4x + 8. y = x y = x + y = x + 3 y = 3x 8 9. Evan had $4 in a savings account at the beginning of the year. At the end of each month, he took $ out of the account. Lisa put $ in her savings account at the beginning of the year. At the end of each month, she put $4 in her account. Let x represent the number of months which have passed and y represent the amount in each savings account. a. Write an equation to represent the amount in Evan s savings account. b. Write an equation to represent the amount in Lisa s savings account. c. Copy and complete the input-output tables through 6 months. Evan s Savings Account Balance Lisa s Savings Account Balance Months, x Total Savings, y Months, x Total Savings, y d. When will Evan and Lisa have the same amount in their savings accounts? How much will they each have at this time? 76 Block 4 ~ Review
Lesson 4.4 ~ Solving Systems by Substitution Solve the system of equations using the substitution method. Show all work necessary to prove that your answer is correct.. x = y +. 3x + y = 9. x + y = 3 3x + y = 8 y = x + 6 x + y = 3. Both of Monique s neighbors owned cows. Mr. James owned five less than three times the number of cows owned by Mr. Peters. The total number of cows owned by both neighbors was 79. Let x represent the number of cows Mr. James owns and y represent the number of cows Mr. Peters owns. a. Explain why the equations x = 3y 5 and x + y = 79 represent this situation. b. Solve the system of equations using the substitution method. How many cows did each neighbor own? Lesson 4.5 ~ Solving Systems Using Elimination Show all work necessary to transform each system of linear equations into a system that is ready for columns to be added together to eliminate a variable. Rewrite the system if it is already set up for elimination. 4. x + y = 5. 3x y = 3 6. 4x + y = 9 x + y = 6 6x + y = 9 x + 3y = Solve each system of equations using the elimination method. Show all work necessary to prove that your answer is correct. 7. x + 3y = 7 8. 5x + 4y = 9. x + y = 7 x 3y = x + 4y = 6 4x 3y = 6 3. Patrick bought one baseball cap and one t-shirt for $36. Sammy bought two baseball caps identical to Patrick s caps along with three of the same t-shirts. Sammy spent a total of $94. a. Explain why the equations x + y = 36 and x + 3y = 94 represent this situation. b. What does x represent based on the equations in part a? What does y represent? c. Solve the system of equations using the elimination method. What are the individual costs for a t-shirt and a baseball cap? Block 4 ~ Review 77
Lesson 4.6 ~ Choosing the Best Method State the best method to solve each system of linear equations and then solve. 3. x + y = 6 3. x = y 33. y = _ 3 x 5 x y = 6 3x + y = 3 y = 4_ 3 x 34. 3x + 4y = 7 35. y = _ x + 3 36. y = x 5 x 8y = 3x + 4y = 8 4x + y = Lesson 4.7 ~ Applications of Systems of Equations Solve each problem using a system of equations. Define the variables and state the solution. Explain how you know your answer is correct. 37. Two jet ski rental companies have different costs. Company A charges a flat fee of $8 plus $.5 per hour. Company B charges a flat fee of $4 plus $. per hour. At what point in time are both rentals the same amount? How much are the rentals for that amount of time? 38. The Mendenhall Theater sells two types of tickets: youth and adult. The theater holds a total of 45 people. One night, the theater sold all their tickets for a total of $,76. Youth tickets cost $4.6 and adult tickets cost $7.. How many tickets of each type did the theater sell that night? 39. Jamal and Emily each started a savings account in January. Jamal started with $46 in his account and added $4 each month. Emily opened her account with $39. Each month she withdrew $5. After how many months will they have the exact same amount in their accounts? How much will be in their accounts at that time? 4. Two girls sold lemonade together. The entire lemonade sale brought in $8. One girl made $4 more than twice the amount the second girl made. How much did each girl make at the lemonade sale? Explain how you know your answer is correct. Lesson 4.8 ~ Systems of Linear Inequalities Graph the solution of each system of linear inequalities. 4. y > 3x + 4 4. y x + 43. y _ 3 x y < _ 3 x 6 y > 5 _ 3 x 4 44. y > 45. y _ x 5 46. y < 3 4x 4 x > y _ 5 4 x + y x 4 78 Block 4 ~ Review
47. Yolanda graphed the system of inequalities where y and y. She said the answers to the system of inequalities was in the middle purple region of the graph below. Do you agree or disagree? Explain your reasoning. Lesson 4.9 ~ Converting Repeating Decimals to Fractions Label each of the following decimals as a terminating decimal or a repeating decimal. 48..4 49.. _ 3 5..5656 Convert each repeating decimal into a fraction. 5.. _ 5 5.. _ 6 53.. 3 54.. 8 55..5 _ 3 56. 7. _ 7 57. Find a repeating decimal that has a value between _ and 3_ 5. Write the value as a fraction and a decimal. Use words and/or numbers to show how you determined your answer. Block 4 ~ Review 79
Ryan Accountant CAREER FOCUS My name is Ryan and I am an accountant. Accountants track financial information for businesses and other organizations. This can mean keeping track of data, preparing reports or using numbers to make predictions. Managers and leaders of businesses depend on accountants to give them accurate information so that they can make decisions that best benefit their organization. Accountants also help organizations with figuring out how much money they will need to pay in taxes. I use math in many ways. I constantly use basic operations to transform raw data into usable information. I have to problem solve in different situations to analyze data for correctness. I also use ratios and fractions to compare how one business is doing as opposed to another. There are a number of types of statistics I use to prepare forecasts and valuations. A Certified Public Accountant must have a 4-5 year degree in accounting. They must also pass a national exam and have a certain number of hours of on-the-job experience in order to get a license. The on-the-job experience can be done while working under the supervision of a CPA who already has a license. The starting salary for an accountant is around $36, per year. Average salaries range between $43, and $67, per year depending on the industry and experience level of the accountant. Salaries for accountants can sometimes reach $5, per year or more. I like the many kinds of organizations and industries an accountant can work in. An accountant can work in government, charity or business. They can be entrepreneurs and open their own public accounting firm, or they can work for a Fortune 5 company. They can work in the entertainment industry or in agriculture. Another benefit to working in accounting is always being a key player in the important decisions that shape and direct the organization you work for. 8 Block 4 ~ Review