Answers. Chapter MHR Answers. d) y 5 2 x 1. y = x + 2. y = 2x + 3. x + y = 3. 5x 3y = 15. y = 2x + 3. y = x x 3y = x.

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1 Answers Chapter Get Read, pages 7. a) 8 e) f). a) e) f). a) 7 7a b. a) 7 a b. a) 8 = + 9 = _ +. a) 9 = + = _ = + = + 7. a) -intercept, -intercept -intercept, -intercept -intercept, -intercept 7 = _ + = = 7 = 7 7 = intercept, -intercept 8 = 7 MHR Answers

2 8. a) = 8 =. a) decreased subtracted minus less than or equal to. a) addition Answers will var.. Answers ma var. For eample: An epression is a combination of numbers, operations, and/or variables that can be evaluated. An equation equates two epressions. 7. C 8. a) (, 7) (, ) (, ) (, 7) 9. a) (, ) (, ) (, ) (, ). a) (, ) (.7, 8) (.,.7) (.9, 7.8) e) (.9,.) f) (.,.7). a) C m C m (, ) + + = 9. a). a) = _ e) Answers ma var. For eample: The point of intersection represents the number of months it will take for the costs to be the same at both clubs. f) Answers ma var. For eample: You should join CanFit because it will be cheaper for ear.. a) C n C 7 n (, 9) Answers ma var. For eample: The cost is the same at both stores when ou rent three video games. The cost is $9.. a) C h C (, ) Jeff charges the same price for h of work as Hesketh s Snow Removal charges for the season.. a) C 7n C 7 n Limestone Hall is less epensive for fewer than guests. e) Answers will var. For eample: convenience of location, parking availabilit, reputation for good food, attractiveness of the hall. a) E 8.n E pairs of jeans. a). L.7 kg g. a) $8 $.8 $. $.. a) 7. Answers will var.. Answers will var.. $ was invested in the account paing %/ear interest and $ was invested in the GIC paing 7.%/ear interest. 7. a) C.d C.d. Connect English With Mathematics and Graphing Lines, pages 8 9. a) 7 ( ). a) d.n l.7p. a) n 7 n 7n n 8 l w 9 The cost of $7 is the same when the Clarkes rent the car from either of the two companies and drive km. Answers MHR

3 8. a) i) E ii) E n iii) E n E Earnings ($s) E = + n (, ) E = n E = Hours of Instruction (s) If Alain is going to give fewer than h of instruction, then package (i) is best. For h, packages (i) and (ii) pa the same amount, $. For more than h but fewer than h, package (ii) pas more. For h, packages (ii) and (iii) pa the same, $. For more than h, package (iii) pas the most. It would not make sense for him to work more than h ( h per week for weeks), because that is the most he can work for packages (ii) and (iii). If he did work more than h, he would have to go with package (i), the flat rate of $. 9. The three lines intersect at the same point.. Answers ma var. For eample: a) No, because the represent the same line and intersect everwhere. No, because the lines are parallel and do not intersect. If two lines have the same slopes and -intercepts, then there is an infinite number of solutions. If two lines have the same slope and different -intercepts, then there is no solution. If two lines have different slopes, then there is one solution.. (, ) and (, ). The second equation is not linear because it has an -term.. a) n. 8%. C. The Method of Substitution, pages 8. a), 9,,,. a) equation : equation : equation : equation : e) either equation : ( ) or equation : ( ). No. (, ) satisfies the first equation but not the second equation.. a), 7, m, n a 8, b e),. a) a a,, b a9, b b (, ) e) (, ) n. Answers ma var. For eample: a) Let S represent the number of hours that Samantha works. Let A represent the number of hours that Adriana works. S A S A 9 Samantha worked h and Adriana worked h. 7. Answers ma var. For eample: a) Let J represent the number of T-shirts bought b Jeff and S represent the number of T-shirts bought b Stephen. Then, J S. S J Jeff bought T-shirts and Stephen bought 9 T-shirts. Jeff spent $.9 and Stephen spent $8.9, before ta. 8. Answers ma var. For eample: a) Let g represent the number of goals and a represent the number of assists. Then, g a 8; g a 7. g, a Ugo scored goals and made assists. 9. Answers ma var. For eample: a) Let C represent the cost of renting a hall and n be the cost of a meal. Then, C n; C 8n. guests.. h. The companies charge the same for km. It is better to rent from Joe s Garage for distances less than km.. Answers ma var. For eample: It is not eas to isolate either of the variables.. Answers ma var. For eample: It is eas to isolate in either equation. Both lines are simple to graph.. a) (, ), (, ), (, ) Eplanations ma var. For eample: Yes, because the slope of the first line, m, and the slope of the third line, m, are negative reciprocals.. wins. Answers ma var. For eample: a) Let C represent the cost of renting a car and d represent the number of kilometres driven. Then, C 9. C.d The costs are the same for driving a distance of km. The mid-size car costs less for driving fewer than km during a -da car rental. e) The full-size car is cheaper b $ adults 9. a) You get 9, which is impossible. Since the lines are parallel and distinct, the lines do not intersect. There is no solution.. a),.,.. (, ); k n. (n )(n ). A. Investigate Equivalent Linear Relations and Equivalent Linear Sstems, pages 9. A and C. C. Answers ma var. For eample: a) ; 9 ; 8 ; ;. MHR Answers

4 . Answers ma var. For eample: l w ; l w. Answers ma var. For eample:.n.d.7; n d 7. The sstems are equivalent because equation is equation divided b, and equation is equation multiplied b. 7. a) Since both sstems have the same solution, (, ), the are equivalent linear sstems. = + = Add: equation equation. Subtract: equation equation. 8. a) Equation was obtained b multipling both sides of equation b three and then subtracting from both sides. Equation was obtained b multipling both sides of equation b three and then adding to both sides. The linear sstem formed b equation and equation is an equivalent linear sstem to the linear sstem formed b equation and equation and has the same point of intersection. You epect to see onl two distinct lines intersecting at the point (, ). 9. Answers will var B. The Method of Elimination, pages. a),,,,. a),,,,. a) (, ) (, ) (, ) (, ). a),,, 9,. a), m, n a, b h, k. a) (, ) (, ) a a, 9 b, b 7. a), 7, a, b u 8, v 8. a) 7 9. a) large bottles 7 small bottles. a) 9, 9, 7 7 Answers will var.. Answers ma var. For eample: Multipl the first equation b and the second equation b, and then subtract the equations. Solve for, substitute this value of into the first equation, and then solve for.. a), a., b. k, n. Answers ma var. For eample: Brent multiplied each equation b to write equivalent equations without decimals. The equivalent equations, without decimals, are easier to solve.,. a), a, b. $. a) $/da $./km 7. a) C.d C 9.d If the drive km, the cost of renting either car is $7. The daughter s suggestion is less epensive. 8. Answers ma var. For eample: You get 8, which is impossible. On a graph, the lines are parallel and distinct so there is no solution.. a) m, n a, b 8 t, w 7 ce bf cd af. (, ) a,, where ae bd. ae bd bd ae b. (,, z) (,, ). Solve Problems Using Linear Sstems, pages 7. crocus bulbs and 8 tulip bulbs. Beta tapes and 7 VHS tapes. cars and vans. $ at 8%/ear and $ at 7.%/ear. Answers ma var. For eample: The numbers are smaller and it is easier to isolate one variable in both equations.. a) Answers will var. (, 77) (, 77) 7. average rowing speed. km/h, speed of current. km/h 8. wind speed km/h, speed of plane km/h 9. L of % milk, L of % cream. L of % sulphuric acid solution, L of % sulphuric acid solution. a) months Kool Karate Karate Klub. medium T-shirts. g of granola with % nuts, g of granola with % nuts. g of metal allo that is % copper, g of metal allo that is % copper. fruit pies, meat pies. $ per meal, $ per da for accommodation 7. best cruise speed km/h, econom cruise speed km/h 8. km 9. g of 8-karat gold, g of 9-karat gold. 8.% Chapter Review, pages 89. a) Let n represent the number of nickels and d represent the number of dimes..n.d. Let M represent Maggie s age and J represent Janice s age. M J 9 Let n represent the number. n 9 n Answers MHR 7

5 . (, ). a) C n C n guests Allison should choose La Casa if she invites more than guests because it will cost less. e) She should choose Hastings Hall if she invites fewer than guests because it will cost less.. a),,,.7,.. chickens. Josie should choose the flat rate if she uses the Internet for more than h per month. 7. males, females 8. B 9. a) (, ) (, ) (, ) (, ). a),, a, b k., h.. Answers will var.. a),.,.,,. a) km Choose compan A for distances greater than km.. $ at %/ear, $8 at.%/ear. average speed of the boat in still water km/h, speed of the current km/h. kg of fertilizer with % nitrogen, kg of fertilizer with % nitrogen 7. Fran earns $8 ; Winston earns $. Chapter Practice Test, pages. a) Let m represent the number of men and w represent the number of women. m w ; m w 7 Let n represent the number. 7 n n. Answers will var.. a) (7, ) 7,. a), a, b, m., n.. a) The second equation is three times, rearranged. Both linear sstems have the same point of intersection, (, ). The first equation is twice, rearranged. The second equation is si times, rearranged.. a),, k, h p., q 8 7. a),, 7,, 8. Answers will var. 9. (.,.), (, ), (.8,.). a) G P G P 8 Gregor works h; Paul works h.. Roll answered 7 questions correctl.. length m, width m. adult $., child $8.. nickels, dimes. The charged $ for h of work.. a), c., d.87, 7. $ at %/ear, $ at %/ear 8. L of % acid solution, 8 L of % acid solution km b bus, 8.7 km b airplane Chapter Get Read, pages. a).. a) 7. a). a). a) 7. a) 7. a) 8. a) 9. a). cm. If P is an point on the right bisector of line segment AB and Q is the point of intersection of AB and the right bisector, then AQ QB and PQA PQB 9. Side PQ is common to PQA and PQB. Therefore, PQA is congruent to PQB (side-angle-side). PA and PB are corresponding sides, so PA PB.. Midpoint of a Line Segment, pages 9. a) (, ) (, ) (, ) a, b. a) (, 8) (, ) (, ) (, ). a) (.9,.8) (.,.) (, ) a, 8 b. a) 7. (.,.9). (, ) 7 8 MHR Answers