Get Ready BLM... Substitute and Evaluate. Evaluate each expression when x = 4 and y =. a) x + 4y b) x y c) 4x + y + 5 d) x y. Evaluate each expression when a = and b =. a) a b + 4 b) a + b 7 c) a b d) b a 4 Simplify Expressions. Simplify. a) x + (x + y) b) 4x (x y) c) a 4b + 6a b d) 4a b (a + 5b) 4. Simplify. a) a (a + b) 4(4a b) b) (x + y) (x y) + 6(x + y) c) 4(x y) 6(x + y) 5(x 6) d) (a + b + c) (a + b c) Graph Lines 5. Graph each line. Use a table of values or the slope and y-intercept method. a) y = x + b) y = x 4 c) y = x+ d) y = x 5 6. Graph each line by first rewriting the equation in the form y = mx + b. a) x + y + = 0 b) x y + 6 = 0 c) x + y 8 = 0 d) x+ y+ =0 7. Graph each line by finding the intercepts. a) x y = 4 b) x + y = c) 4x + y = 4 d) 7x y = 4 BLM Get Ready 8. Graph each line. Choose a convenient method. a) y = x+ 4 b) x 5y = 0 c) x + y = d) y = 5x + 4 Use a Graphing Calculator to Graph a Line 9. Graph each line in question 5 using a graphing calculator. 0. Use your rewritten equations from question 6 to graph each line using a graphing calculator. Percent. Calculate each amount. a) the amount of sugar in 00 g of a 4% sugar IV drip b) the amount of interest owed at the end of a month on an outstanding balance of $500 on a credit card if the company charges.5% per month. Find the simple interest earned after year on each investment. a) $000 invested at % per year b) $5 000 invested at 6% per year c) $900 invested at 4.% per year d) $ 500 invested at.7% per year Use a Computer Algebra System (CAS) to Evaluate Expressions. Evaluate. a) 4x + when x = 0 b) 5y 7 when y = c) z + 6 when z = 4. Use a CAS to check your answers in question. Hint: First substitute x = 4, and then substitute y = in the resulting expression. Use a CAS to Rearrange Equations 5. Use a CAS to check your work in question 6. Copyright 007 McGraw-Hill Ryerson Limited
Section. Practice Master BLM.... Translate each phrase into an algebraic expression. a) six more than three times a number b) five less than one third a value c) a number increased by four, times another number d) a value decreased by the fraction one quarter. Translate each phrase into an algebraic expression. a) three times a length b) fifteen percent of an area c) half a distance d) eleven percent of a mass. Translate each sentence into an algebraic equation. a) Three times a value, decreased by four, is two. b) One third a number, increased by two, is one. c) One number is five times larger than two more than a second number. d) The price of a meal, including fourteen percent tax, is ninety-five dollars and seventy-six cents. 4. Translate each sentence into an algebraic equation. a) At a school concert, 55 tickets were sold. There were 5 more student tickets sold than adult tickets. b) A rectangle has a perimeter of 7 cm. The length of the rectangle is cm longer than twice the width. c) The sum of two times the smaller of two consecutive numbers and three times the larger number is. d) Enrico weighs 7 kg more than Julian. The sum of their masses is 8 kg. 5. Find the point of intersection for each pair of lines. Check your answers. a) y = x + 0 b) y = x y = 4x + 7 y = 9 x c) y = x + d) y = x y = x y = x 5 6. Find the point of intersection for each pair of lines. Check your answers. a) x y = 4 b) x y = x + y = 4 x + y = 4 c) x + y = 4 d) 5x y = 0 x + y = 9 x + y = 7. Use Technology Use a graphing calculator or The Geometer s Sketchpad to find the point of intersection for each pair of lines. Where necessary, round answers to the nearest hundredth. a) x + 5y = 0 b) x + y = 5x y = 5 x + 0y = 5 c) x + y 7 = 0 d) y = 0.5x x 5y = 0 y = 0.5x + 8. Charlene is looking into cell phone plans. Cell Plus gives unlimited minutes for $50/month. A Cell offers a $40 monthly fee, plus 5 /min for any time over 00 min per month. a) Write a linear equation to represent the charges for each company. b) Graph the two equations to find the point of intersection. c) What does the point of intersection represent? d) Which plan should Charlene choose if she estimates that she will use her phone 0 h per month? 6 h per month? BLM Section. Practice Master Copyright 007 McGraw-Hill Ryerson Limited
Section. Practice Master BLM 4.... Solve each linear system using the method of substitution. Check your answers. a) y = x x + y = 6 b) x = 4y 6 x + 6y = 5 c) x + y = 6 x + y = 0 d) 5 = y x 7 = y x. In each pair of linear equations, decide which equation you will use to solve for one variable in terms of the other variable. Do that step. Do not solve the linear system. a) x + y = 6 x + 6y = 5 b) x + y = 7 x + 4y = 5 c) x + y = 4 x + y = 5 d) x 4y = 6 x y =. Is (, ) the solution for the following linear system? Explain how you can tell. x + 6y = y 8x = 4. Solve by substitution. Check your solution. a) x = y + x + y = b) 4x y = 9 y x = 7 c) c d + = 0 c + d + 0 = 0 d) 4x + y = 0 x + y + = 0 5. Simplify each equation, and then solve the linear system by substitution. a) (x + ) (y ) = 6 x + 4(y + ) = 9 b) (x ) (y ) = 0 (x + ) (y 7) = 0 c) (x ) (y + 4) = 7 4( x) ( y) = d) (x ) 4(y + ) = x + (y + ) = 6. The number of tickets sold for a school event is 0. Let a represent the number of adult tickets sold and s represent the number of student tickets sold. The cost of a student ticket is $6 and the cost of an adult ticket is $0. In total, $80 was taken in from ticket sales. a) Write a linear system to represent the information. b) Solve the linear system to find the number of each type of ticket sold. 7. Phoenix Health Club charges a $00 initiation fee, plus $5 per month. Champion Health Club charges a $00 initiation fee, plus $0 per month. a) Write a linear equation to represent the charges for each club. b) Solve the linear system. c) After how many months are the costs the same? d) If you joined a club for only year, which club would be less expensive? BLM 4 Section. Practice Master Copyright 007 McGraw-Hill Ryerson Limited
Section. Practice Master BLM 6.... Which two equations are equivalent? A y = x + 6 B y = x + C y = x + D y = 4x + 6. The following linear system is shown on the graph: y = x + 6 y = x. Write two equivalent equations for each. a) y = 4x + b) x + y = 5 c) x + 5y 6 = 0 d) y = 6x. The perimeter of a rectangle is 0 cm. Write an equation to represent this situation. Then, write an equivalent linear equation. 4. The value of the quarters and nickels in Michael s coin jar is $.65. Write an equation to represent this situation. Then, write an equivalent linear equation. 5. A linear system is given. x y = 7 x + y = 5 Explain why the following is an equivalent linear system. x y = x + 8y = 0 a) Use a graph to show that the following is an equivalent linear system. y = x + 0 = x 9 b) How is equation obtained from equations and? c) How is equation obtained from equations and? BLM 6 Section. Practice Master Copyright 007 McGraw-Hill Ryerson Limited
Section.4 Practice Master BLM 7.... Solve using the method of elimination. a) x y = b) x + y = 4 x + y = x y = c) 4x + y = d) 4x y = 5x y = 8 4x y = 9. Solve using the method of elimination. Check each solution. a) x + y = b) x y = x y = x + y = 9 c) 5x + y = d) 6y 5x = 7 x + y = 9 y 5x = 9. Find the point of intersection of each pair of lines. a) 7x + y = 7 b) x 6y = 6 6x + y = 4 4x y = 6 c) x + y = d) x y = x + y = 4 5x + 6y = 5 4. Solve by elimination. Check each solution. a) (x + ) (y + 7) = 5(x + ) + 4(y ) = 4 b) 5(m ) + (n + 4) = 0 (m + 4) 4(n + ) = c) (a 4) + 5(b + ) = 8 (a ) (b ) = d) (x + ) (y + ) = 6 4(x ) + (y ) = 4 5. Solve each linear system using elimination. a) 0.x + 0.y = 0.5 0.5x 0.4y = 0. b) 0.6a 0.b =.8 0.4a + 0.5b = 0.7 c) 0.x 0.5y =. 0.7x 0.y = 0. d) 0.5x.y =. 4x y = 0.6 6. Solve by elimination. a) = m n m n = 4 x 6 y+ b) + =0 4 x+ y 5 = 7. Some provinces have names with First Nations origins. For example, Ontario comes from an Iroquois word meaning beautiful water. If the number of provincial names with First Nations origins is a, and the number with other origins is b, the numbers are related by the following equations. a + b = 0 a b = 0 a) Interpret each equation in words. b) Find the number of provinces that have names with First Nations origins. 8. At Lisa s Sub Shop, two veggie subs and four roast beef subs cost $4. Five veggie subs and six roast beef subs cost $6. Write and solve a system of equations to find the cost of each type of sub. 9. A weekend at Skyview Lodge costs $60 and includes two nights accommodation and four meals. A week costs $00 and includes seven nights accommodation and ten meals. Write and solve a system of equations to find the cost of one night and the cost of one meal. 0. The Mackenzie, the longest river in Canada, is 056 km longer than the Yukon, the second-longest river. The total length of the two rivers is 746 km. Find the length of each river. BLM 7 Section.4 Practice Master Copyright 007 McGraw-Hill Ryerson Limited
Section.5 Practice Master BLM 9.... The sum of two numbers is 56. One number exceeds the other number by. Find the two numbers.. Three soccer balls and a basketball cost $55. Two soccer balls and three basketballs cost $0. Find the cost of each ball.. The students in the school band are selling chocolate-covered almonds for $ a box and chocolate bars for $ each to raise money for a band trip. Mary sold a total of 96 items and raised $. How many of each did she sell? 4. The cost of printing a magazine is based on a fixed set-up cost and the number of pages to be printed. One printing company charges a $50 set-up fee and $5/page, while a second company charges a $400 set-up fee plus $4/page. a) Write an equation to represent the cost for each company. Define your variables. b) Solve the linear system. c) What does the point of intersection represent? d) Which company should Richard choose to print 75 pages? 5. Joe invests a total of $4000 in two plans. Part of the money is invested at 8% per year and the rest at % per year. The interest paid after year on the % investment is $ more than the interest paid on the 8% investment. How much did Joe invest in each? 6. Monique and Henri work in a factory and earn the same hourly rate and the same overtime rate for hours over 8 h worked in a week. One week, Monique worked 45 h and was paid $8. In the same week, Henri worked 40 h and was paid $7. Find the regular hourly rate and the overtime rate. 7. The cost to rent a car is based on the number of days the car is rented and the number of kilometres it is driven. The cost for a -day rental and 40 km driven is $9. The cost for a 5-day rental and 900 km driven is $65. Find the cost per day and the cost per kilometre. 8. One type of granola is 0% fruit, and another type is 5% fruit. What mass of each type of granola should be mixed to make 600 g of granola that is % fruit? 9. What volume, in millilitres, of a 60% hydrochloric acid solution must be added to 00 ml of a 0% hydrochloric acid solution to make a 6% hydrochloric acid solution? 0. Playing tennis burns energy at a rate of about 5 kj/min. Cycling burns energy at about 5 kj/min. Hans exercised by playing tennis and then cycling. He exercised for 50 min altogether and used a total of 450 kj of energy. For how long did he play tennis?. Erika drove from Ottawa at 80 km/h. Julie left Ottawa h later and drove along the same road at 00 km/h. How far from Ottawa did Julie overtake Erika?. A street has a row of 5 new houses for sale. The middle house is on the most desirable piece of property and is the most expensive. The second house from one end costs $000 more than the first house, the third house costs $000 more than the second house, and so on, up to and including the middle house. The second house from the other end costs $5000 more than the first house, the third house costs $5000 more than the second house, and so on, up to and including the middle house. All the houses on the street cost a total of $ 09 000. What is the selling price of the house at each end of the street? Explain and justify your reasoning. BLM 9 Section.5 Practice Master Copyright 007 McGraw-Hill Ryerson Limited
Chapter Review BLM 0... (page ). Connect English With Mathematics and Graphing Lines. Translate each sentence into an equation. Tell how you are assigning the variables in each. a) Three consecutive numbers add to 75. b) Stephane has loonies and toonies in his pocket totalling $5. c) Three times Jennifer s age is 6 more than Herbert s age.. Write a system of equations for each situation. a) Michael is three times older than his sister Angela. In year, Michael will be twice as old as Angela. How old are the two children today? b) A $ raffle ticket offers a bonus $ early bird draw. 400 tickets were sold for the draw and a total of $894 was collected from ticket sales. How many tickets were bought for $ and how many were bought for $?. Graph each pair of lines to find their point of intersection. a) y = x 5 y = x b) y = x + 8 x + y = c) x y = 4 x + y = 6 d) x y = 8 x y = 4. The Method of Substitution 4. Solve each linear system using the method of substitution. a) x + y = 7 x y = b) y = x + 4 x 4y = 9 c) s + 5t = s + 4t = 4 d) m 6n = m + n = 5. Is the point (, 5) the solution to each system of linear equations? Explain. a) x y = x + 4y = 9 b) x + y = 8 x y = 6. The two largest deserts in the world are the Sahara Desert and the Australian Desert. The sum of their areas is million square kilometres. The area of the Sahara Desert is 5 million square kilometres more than the area of the Australian Desert. Write and solve a system of equations to find the area of each desert.. Investigate Equivalent Linear Relations and Equivalent Linear Systems 7. Which of the following equations is equivalent to y = x+? 5 A y = x + B y = x + C 5y = 0x + D 0x 5y + 5 = 0 BLM 0 Chapter Review Copyright 007 McGraw-Hill Ryerson Limited
8. A linear system is given. y = x 5 y = x+ 7 a) Explain why the following is an equivalent linear system. x 5y = 5 x + 7y = 7 b) If you graph all four lines, what result do you expect? Graph to check. 9. The two most common place names in Canada are Mount Pleasant and Centreville. The total number of places with these names is. The number of places called Centreville is one less than the number of places called Mount Pleasant. Write and solve a system of equations to find the number of places in Canada with each name..4 The Method of Elimination 0. Solve each linear system. Check each solution. a) x y = 4 x + 5y = 7 b) x y = 4 x + y = 5 c) x + 4y = 7 7x y = 7 d) x + 5y = 8 x + 5y 7 = 0. Simplify and solve each system of equations using elimination. a) (x 4) + (y + ) = 8 4(x + ) + 5(y ) = 9 b) 0.4x 0.y = 0.6.8x + 0.4y = 4.4 BLM 0... (page ). Cindy buys a large pizza with two toppings for $.50. Lou buys three large pizzas with four toppings each at the same pizza parlour for $45. Find the cost of a large pizza and the cost per topping..5 Solve Problems Using Linear Systems. A chemist needs 0 L of % salt solution. The chemist has two salt solutions available at 5% and 5% salt. Write and solve a linear system to find the volume of each solution that needs to be combined to make the mixture. 4. Flying into the wind, a plane takes 6 h to fly 000 km. On the return flight, with the same wind, the plane takes 5 h to complete the trip. How fast does the plane fly without any wind, and how fast was the wind blowing? 5. The public golf course runs a junior league with a registration fee of $00 and a cost of $5 per round played. To stay competitive, the private golf club in the same town offers a junior league with a registration fee of $50, but only $0 per round played. a) Write linear equations to represent both junior leagues. b) Solve the linear system. c) Interpret the solution. d) Which league should each golfer join? i) MaeLing plans to play 6 rounds in the league. ii) Jacob plans to play 8 rounds in the league. BLM 0 Chapter Review Copyright 007 McGraw-Hill Ryerson Limited
Chapter Practice Test BLM.... The equation 4x y + 8 = 0 written in slope y-intercept form is A y = x + 4 B y = x 4 C y = x 4 D y = x + 4. An equation equivalent to A 4y = x B y = x C x 4y = 0 D y + 4x = 4 y = x is 4. Translate each sentence into an equation. a) Last year, Raymond was twice as old as Sue. b) The length of a rectangle is five more than three times its width. c) Two less than triple a number is eleven. d) One half of Anne s age ten years from now is fourteen. 4. Solve each linear system by graphing. Check your answers. a) y = x + 5 b) y = x x 5y = y = x 5 c) y = 4x + 4 d) x y = x + 5y = x + y = 5. Solve each linear system using substitution. a) y = x b) x y = x y = 4 x 5y = 9 c) x + y = 6 d) x + y + = 0 x y = x 6y + 9 = 0 6. Solve each linear system using elimination. a) x y = b) 4x + 5y = 4 x + y = 7 x y = c) x + 5y = d) x + y = 8 x y = x + y = 7 7. Solve each system by any method. Check each solution. a) 5x y = 9 b) a + b 4 = 0 x 5y = 4 a 0 = b c) p 6q = 0 d) x + y = 4p + q = 8x + 5y = 6 8. Romano Pizza is selling a large pizza for $4 plus $ per topping. A Slice of Italy Pizza is selling the same size pizza for $ plus $.50 per topping. a) Model the cost at each pizza place with a linear equation. Define your variables. b) Find the point of intersection of the two linear equations. c) Interpret the point of intersection. d) Which place has the better price for a large five-topping pizza? 9. The difference between two numbers is. Twice the smaller number exceeds the larger number by 7. What are the two numbers? 0. A container has 0 bolts in it and has a mass of 65 g. When an additional 5 bolts are placed in the container, the mass is 95 g. Find the mass of a bolt and the mass of the container.. Lawrence is years older than Patrick. Last year, he was twice as old as Patrick. How old is each person now?. White vinegar is a solution of acetic acid in water. There are two strengths of white vinegar a 5% solution and a 0% solution. How many millilitres of each solution must be mixed to make 50 ml of a 9% vinegar solution?. Petr has $5000 invested in two plans. One plan pays 5% simple interest per year and the other pays 8%. At the end of the year, Petr receives a total of $40 in interest. How much did he invest in each plan? BLM Chapter Practice Test Copyright 007 McGraw-Hill Ryerson Limited
Chapter Test BLM.... An equation for the line with slope and y-intercept 4 is A x y = 4 B x y = 4 C x + y = 4 D x + y = 4. The point (, ) is the solution to which linear system? A x + 5y = B x y = x + y = x + 4y = 6 C x y = 5 D 5x + y = x + y = x + 5y = 7. A graph of a linear system is shown. Explain why each of the following is an equivalent linear system to the system shown in the graph. a) y = x 4 b) x = 7.5 y = y = x 5 c) x y = x 4y = 4. Write a linear system for each situation. a) Jim is three times as old as Allison. Two years ago, the sum of their ages was 6. b) Two numbers add together to give 4 and differ by 4. c) The perimeter of a rectangle is cm. The length is cm more than the width. d) Erin earns twice as much as Michael every week. Last week, their earnings added to $09.40. 5. Solve each linear system by graphing. a) y = x + b) 4x + y = 7 x y = 4x y = c) x + y = d) x + y = 4 x + 4y = 4 x = 0 y 6. Solve each linear system using substitution. a) y = x 4 b) y = x 9 x + 5y = x y = 4 c) x y = 5 d) 7 = b a x + y = 4 = a + b 7. Solve each system using elimination. a) x + y = 4 b) x 4y = x y = 8 x + y = 4 c) 5x + 7y = d) c + d = x + y = c + d = 8. Monique s swimming pool filter needs repair. She calls two companies for prices. The Pool BoyZ charge $70 for a service call and $40/h for labour. KemiKal Balance charge $50 for a service call and $45/h for labour. a) Write a linear equation for each company. b) Graph the two lines on the same set of axes and find the point of intersection. c) Interpret this point of intersection. d) If the repair will take.5 h, which company should Monique use? 9. Donny is combining two nut mixtures to create a new mixture. Both mixes are a combination of peanuts and almonds. The first mixture is 40% almonds and the second is 5% almonds. How much of each mixture should Donny combine to make 6 kg of a mixture of % almonds? BLM Chapter Test Copyright 007 McGraw-Hill Ryerson Limited
BLM Answers BLM 5... (page ) Get Ready. a) 4 b) 6 c) 0 d) 4. a) b) 0 5 c) d) 5. a) 5x + y b) x + y c) 9a 6b d) 6a 8b 4. a) a b b) x + 5y c) x 6y + 0 d) a b + 5c 5. a) 6. a) y = x b) y = x+ b) c) y = x+ 6 c) d) Chapter Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
d) y = x 6 c) x-intercept 6, y-intercept 8 BLM 5... (page ) d) x-intercept, y-intercept 7 7. a) x-intercept 4, y-intercept 4 8. a) b) x-intercept 4, y-intercept 6 b) Chapter Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
c) d). a) 8 g b) $5.50. a) $60 b) $900 c) $86.40 d) $499.50. a) b) c) 9 Section. Practice Master. a) x + 6 b) 5 n c) (x + 4)y d) p 4. a) l b) 0.5A c) d d) 0.m BLM 5... (page ) 9. a) y = x + b) c) y = x+ d) 0. a) y = x b) c) y = x+ 6 d) y = x 4 y = x 5 y = x+ y = x 6. a) x 4 = b) = n + c) x = 5(y + ) d).4x = 95.76 4. a) a + a + 5 = 55 b) (w + w + ) = 7 c) x + (x + ) = d) j + j + 7 = 8 5. a) (, 9) b) (5, 4) c) (, ) d) (, ) 6. a) (7, ) b) (, ) c) (, ) d) (, 0) 7. a) ( 4.5,.6) b) (.54, 0.8) c) (.89, 0.6) d) (.67, 0.) 8. a) C = 50; C = 40 + 0.05t; C is the monthly charge and t is time, in minutes, over 00 min/month b) (00, 50) c) Both plans cost $50 for 500 min/month (00 min + 00 min). d) Cell Plus; A Cell Section. Practice Master. a) (, ) b) ( 8, 7) c) (, ) d) (, ). a) Solve x + 6y = 5 for x; x = 5 6y. b) Solve x + y = 7 for y; y = 7 x. c) Solve x + y = 4 for x; x = y 4. d) Solve x y = for x or y; x = + y or y = x.. Yes. The point satisfies both equations. 4. a) (, ) b) ( 7, 9) c) (, ) d) (, 4 7 7) 5. a) (, 9 7 7) b) (4, 5) c) (., 6.) d) (, ) 6. a) a + s = 0; 6a + 0s = 80 b) 0 adult tickets and 00 student tickets 7. a) C = 5t + 00; C = 0t + 00; C is the cost and t is time, in minutes. b) (0, 500) c) 0 months d) Champion Health Club Chapter Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
Section. Practice Master. A and D. Answers may vary. For example: a) y = 8x + 6; y = x + 9 b) 6x + 4y = 0; 9x + 6y = 5 c) 4x + 0y = 0; 4x 0y + = 0 y d) y = x 6; = x. Answers may vary. For example: (l + w) = 0; l + w = 5 4. Answers may vary. For example: 0.5q + 0.05n =.65; 5q + n = 5. Equation is equation multiplied by. Equation is equation multiplied by 4. 6. a) The four lines pass through the same point. b) Equation is the sum of equations and. c) Equation is equation minus equation. Section.4 Practice Master. a) (5, 4) b) (, ) c) (, ) d) (0, ). a) (, ) b) (9, 6) c) (, ) d) (5, ). a) (, ) b) (0, 6) c) (, ) d) (, 0) 4. a) (, ) b) (, 6) c) (, ) d) (, ) 5. a) (, ) b) 5 (, 57 ) c) (, ) d) ( 0.4,.) 6. a) (, 6) b) (, ) BLM 5... (page 4) 7. a) There are 0 provinces. Three times the number of provinces with names with First Nations origins minus twice the number of names with other origins is zero. b) 4 8. veggie sub $5, roast beef sub $6 9. Let n represent the cost of one night s accommodation and m represent the cost of one meal. n + 4m = 60 7n + 0m = 00 Solution: (50, 5) One night s accommodation costs $50 and one meal costs $5. 0. The Mackenzie is 44 km long and the Yukon is 85 km long. Section.5 Practice Master. 7, 9. soccer ball $5, basketball $50. chocolate almonds 4, chocolate bars 55 4. a) C = 5p + 50; C = 4p + 400; C is the cost and p is the number of pages. b) (50, 000) c) Printing 50 pages costs $000 at both companies. d) the second company 5. $800 at %; $00 at 8% 6. regular rate $7.50, overtime rate $4 7. $5/day; $0.0/km 8. 40 g of 0% fruit; 60 g of 5% fruit 9. 5 ml 0. 0 min. 500 km. Let the cost of the middle house be m. Write expressions for all the other houses, and solve an equation with the sum of the expressions on one side and the total cost of all the houses on the other side. The house on one end costs $00 000 and the house on the other end costs $86 000. Chapter Review. a) Let the middle number be x. x + x + x + = 75 b) Let l represent the number of loonies and t represent the number of toonies. l + t = 5 c) Let j represent Jennifer s age and h represent Herbert s age. j = h + 6. a) m = a; m + = (a + ) b) x + y = 400; x + y = 894. a) (4, ) b) (, ) c) (,5 ) d) (, ) 4. a) (5, ) b) (, ) c) (4, ) d) (, ) Chapter Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited
5. a) Yes. The point satisfies both equations. b) No. The point only satisfies the first equation. 6. Sahara Desert: 9 million square kilometres; Australian Desert: 4 million square kilometres 7. C 8. a) Equation is equation multiplied by 5 and rearranged. Equation is equation multiplied by 7 and rearranged. b) Equation and equation represent the same line. Equation and equation represent the same line. 9. Mount Pleasant 6, Centreville 5 0. a) (9, 5) b) (, ) c) (, ) d) (, 4). a) (, 4) b) (, ). cost of a large pizza $, cost per topping $0.75. 4 L of 5% salt and 6 L of 5% salt 4. plane speed 550 km/h, wind speed 50 km/h 5. a) C = 5r + 00; C = 0r + 50 b) (0, 450) c) It costs $450 for 0 rounds at both clubs. d) i) private club ii) public club Chapter Practice Test. D. C. a) R = (S ) b) l = w + 5 c) x = d) ( 0) = 4 a + 4. a) (, ) b) (4, ) c) (, 0) d) (, ) 5. a) (6, ) b) ( 9, 40 9 9 ) c) (, ) d) (, ) 6. a) (, 8) b) 6 (, 8) c) (, ) d) (, ) 7. a) (, ) b) (, ) c) (, ) d) ( 4, ) 7 7 8. a) C = t + 4; C =.5t + ; C is the cost and t is the number of toppings. b) (4, 8) c) A four-topping large pizza costs $8 at both places. d) Romano Pizza 9. 6, 9 0. bolt 0 g, container 5 g. Lawrence 5, Patrick. 0 ml of the 5% solution and 40 ml of the 0% solution. $000 at 5%/year and $000 at 8%/year Chapter Test BLM 5... (page 5). D. B. a) These are the equations of the lines written in slope and y-intercept form. b) This system has the same solution as the graphed system. c) This system has the same solution as the graphed system. 4. a) j = a; j + a = 6 b) x + y = 4; x y = 4 c) (l + w) = ; l = w + d) e = m; e + m = 09.40 5. a) (, 5) b) (, ) c) (0, ) d) (, ) 6. a) (, ) b) (5, ) c) (, ) d) (, 5) 7. a) (, 6) b) (, ) c) (, ) d) (, ) 8. a) C = 40t + 70; C = 45t + 50 b) c) Both companies charge $0 for a 4-h service call. d) KemiKal Balance 9.. kg of 40% almonds and.8 kg of 5% almonds Chapter Practice Masters Answers Copyright 007 McGraw-Hill Ryerson Limited