Name Date Chapter 4 Fair Game Review Solve the equation. Check our solution.. 8 3 = 3 2. 4a + a = 2 3. 9 = 4( 3k 4) 7k 4. ( m) 2 5 6 2 = 8 5. 5 t + 8t = 3 6. 3 5h 2 h + 4 = 0 2 7. The profit P (in dollars) from selling calculators is P = ( + ) How man calculators are sold when the profit is $425? 25 0 250. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 79
Name Date Chapter 4 Fair Game Review (continued) Graph the inequalit in the coordinate plane. 8. 9. < 3 0. 4 > 7. 2 + 3 6 2. Your boat has a weight limit of 200 pounds. Suppose an average adult weighs 50 pounds and an average child weighs 00 pounds. a. Use a model to write an inequalit that represents this situation. b. Graph the inequalit. c. There are 4 adults and 5 children on the boat. Is the boat safe? Eplain. 80 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 4. Solving Sstems of Linear Equations b Graphing For use with Activit 4. Essential Question How can ou solve a sstem of linear equations? ACTIVITY: Writing a Sstem of Linear Equations Work with a partner. Your famil starts a bed-and-breakfast. The spend $500 fiing up a bedroom to rent. The cost for food and utilities is $0 per night. Your famil charges $60 per night to rent the bedroom. a. Write an equation that represents the costs. Cost, C (in dollars) = $0 per night Number of nights, + $500 b. Write an equation that represents the revenue (income). Revenue, R (in dollars) = $60 per night Number of nights, c. A set of two (or more) linear equations is called a sstem of linear equations. Write the sstem of linear equations for this problem. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 8
Name Date 4. Solving Sstems of Linear Equations b Graphing (continued) 2 ACTIVITY: Using a Table to Solve a Sstem Use the cost and revenue equations from Activit to find how man nights our famil needs to rent the bedroom before recovering the cost of fiing up the bedroom. This is the break-even point. a. Complete the table. 0 2 3 4 5 6 7 8 9 0 C R b. How man nights does our famil need to rent the bedroom before breaking even? 3 ACTIVITY: Using a Graph to Solve a Sstem a. Graph the cost equation from Activit. 600 b. In the same coordinate plane, graph the revenue equation from Activit. 500 400 300 c. Find the point of intersection of the two graphs. What does this point represent? How does this compare to the break-even point in Activit 2? Eplain. 200 00 0 0 2 3 4 5 6 7 8 9 0 2 82 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 4. Solving Sstems of Linear Equations b Graphing (continued) 4 EXAMPLE: Using a Graphing Calculator Use a graphing calculator to solve the sstem. = 0 + 500 Equation = 60 Equation 2 a. Enter the equations into our b. To find the solution, use calculator. Then graph the the intersect feature to equations in an appropriate find the point of intersection. 0, 60. window. The solution is at ( ) 800 = 0 + 500 = 60 0 0 6 What Is Your Answer? 5. IN YUR WN WRDS How can ou solve a sstem of linear equations? How can ou check our solution? 6. Solve one of the sstems b using a table, another sstem b sketching a graph, and the remaining sstem b using a graphing calculator. Eplain wh ou chose each method. a. = 4.3 +.2 b. = c. = 5 =.7 2.4 = 2 + 9 = 3 + Copright Big Ideas Learning, LLC Big Ideas Math Algebra 83
Name Date 4. Practice For use after Lesson 4.. Use the table to find the break-even point. Check our solution. C = 25 + 20 R = 60 0 2 3 4 5 6 7 8 C R Solve the sstem of linear equations b graphing. 2. = 3 + 3. = 4 + = 2 4 = 5 8 Use a graphing calculator to solve the sstem of linear equations. 2 4. = + 2 5. = 7 3 = 4 + = 3 6. There are 26 students in our class. There are 4 more girls than bos. Use a sstem of linear equations to find how man bos are in our class. How man girls are in our class? 84 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 4.2 Solving Sstems of Linear Equations b Substitution For use with Activit 4.2 Essential Question How can ou use substitution to solve a sstem of linear equations? ACTIVITY: Using Substitution to Solve a Sstem Work with a partner. Solve each sstem of linear equations using two methods. Method : Solve for first. Solve for in one of the equations. Use the epression for to find the solution of the sstem. Eplain how ou did it. Method 2: Solve for first. Solve for in one of the equations. Use the epression for to find the solution of the sstem. Eplain how ou did it. Is the solution the same using both methods? a. 6 = b. 2 3 = c. 3 + = 5 2 + 3 = 7 = 5 4 = 3 d. 5 = 2 e. + = f. 2 6 = 6 3 6 = 2 5 + = 3 7 8 = 5 Copright Big Ideas Learning, LLC Big Ideas Math Algebra 85
Name Date 4.2 Solving Sstems of Linear Equations b Substitution (continued) 2 ACTIVITY: Writing and Solving a Sstem of Equations Work with a partner. a. Roll a pair of number cubes that have different colors. Then write the ordered pair shown b the number cubes. The ordered pair at the right is (3, 4). b. Write a sstem of linear equations that has this ordered pair as its solution. -value -value c. Echange sstems with our partner and use one of the methods from Activit to solve the sstem. 3 ACTIVITY: Solving a Secret Code Work with a partner. Decode the quote b Archimedes., 8 7 7 5 4 5 3 2 3 0 5 2 3 3 4 5. 3 4 5 7 6 7 4 2 7 5 8 5 5 3 9 8 86 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 4.2 Solving Sstems of Linear Equations b Substitution (continued) ( ) A, C 3 + = ( ) D, E 0 + = ( ) G, H + = 0 = 3 = 0 = 6 ( ) I, L 2 9 + = ( ) M, N 2 4 + = ( ), P + 2 = 2 2 = 3 2 = 2 2 = 6 ( ) R, S 2 2 + = ( ) T, U 2 7 + = ( ) V, W 2 + = 20 = 6 = 0 = What Is Your Answer? 4. IN YUR WN WRDS How can ou use substitution to solve a sstem of linear equations? Copright Big Ideas Learning, LLC Big Ideas Math Algebra 87
Name Date 4.2 Practice For use after Lesson 4.2 Solve the sstem of linear equations b substitution. Check our solution. 3. = 2 + 4 2. 5 7 4 = + 3 = 9 = 4 + 2 3. 5 = 4 4. 2 + 3 = 0 2 + 2 = 6 8 + 9 = 8 5. A gas station sells a total of 4500 gallons of regular gas and premium gas in one da. The ratio of gallons of regular gas sold to gallons of premium gas sold is 7 : 2. a. Write a sstem of linear equations that represents this situation. b. How man gallons sold were regular gas? premium gas? 88 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 4.3 Solving Sstems of Linear Equations b Elimination For use with Activit 4.3 Essential Question How can ou use elimination to solve a sstem of linear equations? ACTIVITY: Using Elimination to Solve a Sstem Work with a partner. Solve each sstem of linear equations using two methods. Method : Subtract. Subtract Equation 2 from Equation. What is the result? Eplain how ou can use the result to solve the sstem of equations. Method 2: Add. Add the two equations. What is the result? Eplain how ou can use the result to solve the sstem of equations. Is the solution the same using both methods? a. 2 + = 4 b. 3 = 4 c. + 2 = 7 2 = 0 3 + = 2 2 = 5 2 ACTIVITY: Using Elimination to Solve a Sstem Work with a partner. 2 + = 2 Equation + 5 = Equation 2 a. Can ou add or subtract the equations to solve the sstem of linear equations? Eplain. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 89
Name Date 4.3 Solving Sstems of Linear Equations b Elimination (continued) b. Eplain what propert ou can appl to Equation in the sstem so that the coefficients are the same. c. Eplain what propert ou can appl to Equation 2 in the sstem so that the coefficients are the same. d. You solve the sstem in part (b). Your partner solves the sstem in part (c). Compare our solutions. e. Use a graphing calculator to check our solution. 3 ACTIVITY: Solving a Secret Code Work with a partner. Solve the puzzle to find the name of a famous mathematician who lived in Egpt around 350 A.D. 4 B W R M F Y K N 3 J A S I D X Z 2 Q P C E G B T J M R C Z N U W 0 K X U H L Y S Q F E A S W K R M 2 G J Z N H V D G 3 E L X L F Q B 3 2 0 2 3 4 2 + = 0 = 3 + = 2 2 2 = 4 3 + 3 = 0 2 2 = 8 2 + = 3 = 0 + = 4 = 2 + = 5 = + 2 = 5 2 = 5 90 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 4.3 Solving Sstems of Linear Equations b Elimination (continued) What Is Your Answer? 4. IN YUR WN WRDS How can ou use elimination to solve a sstem of linear equations? 5. When can ou add or subtract equations in a sstem to solve the sstem? When do ou have to multipl first? Justif our answers with eamples. 6. In Activit 2, wh can ou multipl the equations in the sstem b a constant and not change the solution of the sstem? Eplain our reasoning. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 9
Name Date 4.3 Practice For use after Lesson 4.3 Solve the sstem of linear equations b elimination. Check our solution.. + = 7 2. 2 5 = 8 3 = 2 + = 6 3. 8 9 = 7 4. 5 + 3 = 6 2 3 = 5 9 4 = 5. A high school has a total of 850 students. There are 60 more female students than there are male students. a. Write a sstem of linear equations that represents this situation. b. How man students are female? male? 92 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 4.4 Solving Special Sstems of Linear Equations For use with Activit 4.4 Essential Question Can a sstem of linear equations have no solution? Can a sstem of linear equations have man solutions? ACTIVITY: Writing a Sstem of Linear Equations Work with a partner. Your cousin is 3 ears older than ou. Your ages can be represented b two linear equations. = t Your age 2 = t + 3 Your cousin s age a. Graph both equations in the same coordinate plane. b. What is the vertical distance between the two graphs? What does this distance represent? 0 8 6 4 2 0 0 2 4 6 8 0 2 t c. Do the two graphs intersect? If not, what does this mean in terms of our age and our cousin s age? 2 ACTIVITY: Using a Table to Solve a Sstem Work with a partner. You invest $500 for equipment to make dog backpacks. Each backpack costs ou $5 for materials. You sell each backpack for $5. a. Complete the table for our cost C and our revenue R. 0 2 3 4 5 6 7 8 9 0 C R Copright Big Ideas Learning, LLC Big Ideas Math Algebra 93
Name Date 4.4 Solving Special Sstems of Linear Equations (continued) b. When will our compan break even? What is wrong? 3 ACTIVITY: Using a Graph to Solve a Puzzle Work with a partner. Let and be two numbers. Here are two clues about the values of and. Clue : Clue 2: Words The value of is 4 more than twice the value of. The difference of 3 and 6 is 2. Equation = 2 + 4 3 6 = 2 a. Graph both equations in the same coordinate plane. b. Do the two lines intersect? Eplain. 5 4 3 2 5 4 3 2 2 3 4 5 c. What is the solution of the puzzle? 2 3 4 5 d. Use the equation = 2 + 4 to complete the table. 0 2 3 4 5 6 7 8 9 0 94 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 4.4 Solving Special Sstems of Linear Equations (continued) e. Does each solution in the table satisf both clues? f. What can ou conclude? How man solutions does the puzzle have? How can ou describe them? What Is Your Answer? 4. IN YUR WN WRDS Can a sstem of linear equations have no solution? Can a sstem of linear equations have man solutions? Give eamples to support our answers. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 95
Name Date 4.4 Practice For use after Lesson 4.4 Solve the sstem of linear equations.. = 2 5 = 2 + 7 2. 3 + 4 = 0 3 5 = 4 2 3. = 8 4. 3 = 6 + 4 2 = 2 6 2 + = 9 5. You start reading a book for our literature class two das before our friend. You both read 0 pages per night. A sstem of linear equations that represents this situation is = 0 + 20 and = 0. Will our friend finish the book before ou? Justif our answer. 6. You and a friend bu music from different online stores. The sstem of linear equations represents the total amount spent on songs and albums. Both of ou bu the same number of albums. Compare the number of songs each of ou bu. 0.95 + 0 = 39.5.9 + 20 = 79 96 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date Etension 4.4 Practice For use after Etension 4.4 Use a graph to solve the equation. Check our solution.. 3 4 = 2. 3 4 8 3 + = 3. 4 2 + = 4. + = 4 2 5. n the first da of our garage sale, ou earned 2 + 9 dollars. The net da ou earned 22 dollars. Is it possible that ou earned the same amount each da? Eplain. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 97
Name Date Etension 4.4 Practice (continued) 6. You hike uphill at a rate of 200 feet per minute. Your friend hikes downhill on the same trail at a rate of 250 feet per minute. How long will it be until ou meet? 800 ft 00 ft Not drawn to scale 7. Two savings accounts earn simple interest. Account A has a beginning balance of $500 and grows b $25 per ear. Account B has a beginning balance of $750 and grows b $5 per ear. Growth rate Years, + Beginning balance = Growth rate Years, + Beginning balance a. Use the model to write an equation. b. After how man ears do the accounts have the same balance? 98 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 4.5 Sstems of Linear Inequalities For use with Activit 4.5 Essential Question How can ou sketch a graph of a sstem of linear inequalities? ACTIVITY: Graphing Linear Inequalities Work with a partner. Match the linear inequalit with its graph. 2 + 4 Inequalit 2 0 Inequalit 2 a. b. 4 3 2 5 4 3 2 5 4 3 2 3 4 5 5 4 3 2 2 3 4 5 2 3 4 5 3 4 5 2 ACTIVITY: Graphing a Sstem of Linear Inequalities Work with a partner. Consider the sstem of linear inequalities given in Activit. 2 + 4 Inequalit 2 0 Inequalit 2 4 3 2 Use colored pencils to shade the solutions of the two linear inequalities. When ou graph both inequalities in the same coordinate plane, what do ou get? 5 4 3 2 3 4 5 3 4 5 Describe each of the shaded regions in the graph at the right. What does the unshaded region represent? Copright Big Ideas Learning, LLC Big Ideas Math Algebra 99
Name Date 4.5 Sstems of Linear Inequalities (continued) 3 ACTIVITY: Writing a Sstem of Linear Inequalities Work with a partner. Write a sstem of 4 linear inequalities whose solution is the traffic sign at the right. () + 5 3 2 5 4 3 2 2 3 4 5 (2) + 2 3 5 (3) (4) 4 ACTIVITY: Representing a State b a Linear Sstem Two states can be represented as the graph of a sstem of linear inequalities. Identif the two states. Eplain our reasoning. 00 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
Name Date 4.5 Sstems of Linear Inequalities (continued) What Is Your Answer? 5. IN YUR WN WRDS How can ou sketch the graph of a sstem of linear inequalities? 6. When graphing a sstem of linear inequalities, which region represents the solution of the sstem? Do ou think all sstems have a solution? Eplain. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 0
Name Date 4.5 Practice For use after Lesson 4.5 Graph the sstem of linear inequalities.. > 2 + 2 2. + 3 2 + > 4 3. 3 0 4. 4 > 3 8 + 3 2 9 + 3 2 5. You have at most 0 hours to stud for our math and English finals. You decide to stud at least 3 times as much for math as ou do for English. a. Write and graph a sstem of linear inequalities that represents this situation. b. Is it possible to stud 7 hours for math and 3 hours for English in this situation? Justif our answer. 02 Big Ideas Math Algebra Copright Big Ideas Learning, LLC