Download Chapter 1 Diagnostic Test

Chapter 1 Diagnostic Test
STUDENT BOOK PAGES 4–7
1. Complete the table of values for the linear relation
3x + 2y = 18.
2. Graph the relation 5y – 4x = 60 by determining its
x- and y-intercepts.
x
–2
y
12
4
0
6
10
–3
0
3. a) Using a graphing calculator, enter the relation y = –3x + 7 into the equation editor as Y1.
Press GRAPH to view the graph of the relation.
b) Determine the slope and y-intercept of the relation 12x + 4y = 16. Predict how the graph
of this relation would compare with the graph of the relation in part a).
c) Write the relation in part b) in the form y = mx + b, enter it as Y2, and press GRAPH.
Explain what you see.
4. a) To graph the equation 3x – 6y = 9, would you determine the x- and y-intercepts or would you
determine the slope and y-intercept? Explain your choice.
x y
b) You suspect that the equations 4y – 3x + 12 = 0 and − = 1 have identical graphs.
4 3
Describe a strategy you could use to decide whether your suspicion is correct.
5. Expand and simplify as necessary.
a) 12x – 10 – 7x – 5 b) 4(–2x + 7)
c) (2x – 3) – (5x – 4) d) 3(x + 7) – 5(6 – 2x)
6. Solve.
a) x – 5 = –3
c) 3x – 10 = –2x
b) 26 = –2x – 8
d) 3x + 5 = 5x + 17
Copyright © 2011 by Nelson Education Ltd.
7. Consider the equations y = m1x + 4 and y = m2x – 2. For what values of m1 and m2 will the
graphs of these two equations be identical? For what values will the graphs be parallel?
Explain your answers.
Chapter 1 Diagnostic Test | 1
Chapter 1 Diagnostic Test Answers
1.
x
–2
4
2
0
8
6
10
y
12
3
6
9
–3
0
–6
2.
x-intercept: –15; y-intercept: 12
3. a)
4. a) Answers may vary, e.g., I prefer x- and
y-intercepts because the equation will not
need to be rearranged.
b) Answers may vary, e.g., I could determine
the x- and y-intercepts of both lines, and then
compare them to see if they are equal.
5. a) 5x – 15
b) –8x + 28
c) –3x + 1
d) 13x – 9
6. a) x = 2
b) x = –17
c) x = 2
d) x = –6
7. The graphs will never be identical because they
have different y-intercepts. They will be parallel
only when m1 = m2 because the slopes are the
same for parallel lines.
The two lines are parallel because they have
the same slope but different y-intercepts.
If students have difficulty with the questions on the Diagnostic Test, it may be necessary
to review the following topics:
• expanding and simplifying algebraic expressions
• graphing a linear relation, given the x- and y-intercepts
• graphing a linear equation, given the y-intercept and the slope
• solving linear equations
2 | Principles of Mathematics 10: Chapter 1 Diagnostic Test Answers
Copyright © 2011 by Nelson Education Ltd.
b) slope: –3; y-intercept: 4; same slope,
different y-intercept (i.e., parallel)
c) y = –3x + 4
Lesson 1.1 Extra Practice
STUDENT BOOK PAGES 8–14
1. The ordered pair (c, c) satisfies the relation
3x – y = 8. What is the value of c?
2. Define variables for each situation, and write an
equation to represent the situation.
a) Alexia earns $7.00/h gardening for her aunt
and $8.50/h babysitting. Last month, she
earned $98.50.
b) Dieter has a long-distance plan that costs
$4.95/month, plus 4¢/min for long-distance
calls within Canada and the U.S., and 5¢/min
for calls to Europe. Last month, Dieter’s total
spending on long-distance calls was $11.95.
Copyright © 2011 by Nelson Education Ltd.
3. Graph each equation for question 2.
4. Justin buys almonds at 2.25¢ per gram and dried
apricots at 1.5¢ per gram to make a snack mix.
He spends $6.00 in total.
a) Write an equation to represent this situation,
using x for the amount of almonds, in grams,
and y for the amount of dried apricots, in
grams.
b) Use a graphing calculator to graph your
equation. Remember to use appropriate
window settings.
c) Set up and display a table of values for your
equation to help you determine the amount of
dried apricots Justin bought if he bought
250 g of almonds.
5. One year ago, Renata invested some of her
income in two investment accounts: a
guaranteed-income fund that pays a return of
4% per year and a high-growth account that, for
the year just past, paid out 6%. Renata’s return
on her investment is $360. Use two different
strategies to represent Renata’s possible
investments in each account.
6. Marta works for a company that makes floral
arrangements for special events. She is
negotiating a new plan for her travelling
expenses and suggests 15¢/km as a fair rate.
The company suggests an alternative plan of
12¢/km, with an additional flat payout of
$12.50/month. In a typical month, Marta drives
700 km on company business. Which plan is
better for Marta?
Lesson 1.1 Extra Practice | 3
Lesson 1.1 Extra Practice Answers
1. c = 4
2. a) Let x represent the number of hours spent
gardening, and let y represent the number
of hours spent babysitting.
7.00x + 8.50y = 98.50
b) Let x represent the number of minutes
spent on calls within Canada or the U.S.,
and let y represent the number of minutes
spent on calls to Europe.
0.04x + 0.05y + 4.95 = 11.95
5. Answers may vary, e.g.,
Table of values:
x
0
1500
3000
4500
6000
7500
9000
y
6000
5000
4000
3000
2000
1000
0
Graph:
3. a)
Equation: 0.04x + 0.06y = 360
Graphing calculator:
4. a) 2.25x + 1.50y = 600
b)
6. The plan that Marta suggested is better.
c)
4 | Principles of Mathematics 10: Lesson 1.1 Extra Practice Answers
Copyright © 2011 by Nelson Education Ltd.
b)
Lesson 1.2 Extra Practice
STUDENT BOOK PAGES 15–20
1. DriveEasy, a car share-rental
company, rents vehicles
online on a sliding scale, as
shown in the graph.
a) How much does it cost to
rent a car for 1 h 45 min?
b) For how long can you rent
a car if you have $18.00?
2. a) Write an equation for the
linear relation in
question 1.
b) Use your equation to
calculate the answers for
question 1.
c) Compare your original
answers for question 1 with your answers for
part b). Identify one advantage of each
strategy.
5. Nita is comparing two job offers. Roxie’s
Boutique is offering $3000/month plus 25%
commission on sales, and Cherie Womenswear
is offering $2400/month plus 40% commission
on sales. Compare the two offers. Which job
should Nita take? Explain your decision.
6. A train leaves Montréal for Toronto at
9:30 a.m., travelling at 120 km/h. At the same
time, a train bound for Montréal leaves Toronto,
travelling at 105 km/h. The distance from
Montréal to Toronto by train is 520 km.
a) Describe two strategies you could use to
estimate when the trains will pass each other.
b) Use one of your strategies to estimate when
the trains will pass each other.
Copyright © 2011 by Nelson Education Ltd.
3. This graph shows the relationship between the
cost of a safari tour and the number of tourists.
4. Benoit drove at 85 km/h from Barrie to
Sudbury. At this speed, his truck uses gas at a
rate of 7.5 L/100 km. Benoit left Barrie with
40 L of gas in the tank, and his low fuel warning
light came on when 4 L was left. Estimate how
long after leaving Barrie the warning light
came on.
a) Write an equation for the relation.
b) Use your equation to determine the cost
of a safari for six people.
c) How many tourists can go on a safari for
$1250? How many can go for 1850?
d) Is it possible for a safari to cost $1600?
Explain.
Lesson 1.2 Extra Practice | 5
Lesson 1.2 Extra Practice Answers
1. a) about $8.60
b) about 4 h 20 min
2. a) y = 3.5x + 2.5
b) $8.63, 4 h 26 min
c) Answers may vary, e.g., using the graph to
estimate is quicker, but using the equation is
more accurate.
3. a) y = 800 + 150x
b) $1700
c) 3 tourists, 7 tourists
d) no, because the corresponding x-value is not
a whole number
6. a) Answers may vary, e.g., drawing a graph of
the distances of the two trains from either
Montréal or Toronto; creating a table of
values of these distances and determining
when these values are equal; writing
expressions to represent the distances
travelled by the trains, setting the sum of the
two expressions for distance equal to 520,
and solving for time.
b) Answers may vary, e.g., about 11:50 a.m.
4. Answers may vary, e.g., about 5 h 40 min
Copyright © 2011 by Nelson Education Ltd.
5. Roxie’s pays more than Cherie Womenswear
for up to $4000/month in sales. If Nita thinks
that she can sell more than $4000, she should
choose Cherie Womenswear’s offer; otherwise
she should choose Roxie’s offer.
6 | Principles of Mathematics 10: Lesson 1.2 Extra Practice Answers
Lesson 1.3 Extra Practice
STUDENT BOOK PAGES 21–28
1. Which ordered pair is a solution to the system of
equations x + 2y = 6 and y = 8 – 3x?
a) (–2, 2) b) (0, 8) c) (0.5, 6.5) d) (2, 2)
2. Which system of equations matches the graph
shown?
a) 3x + y = 2 and 2x – 3y = 6
b) 3x – y = 2 and 2x + 3y = 12
c) 2x – 3y = 12 and y = 3x – 2
d) y = 3x – 2 and 2x + 3y = 6
Copyright © 2011 by Nelson Education Ltd.
3. a) Graph the system 3x – y = 5 and x + 2y = 4
by hand.
b) Solve the system using your graph.
c) Verify your solution by substituting into the
given equations.
4. Use graphing technology to graph and solve the
system 2x – 5y = 3 and x + y = 12.
5. A passenger airplane takes 4 h 15 min for a
journey of 3600 km. The airplane travels at a
cruising speed of 900 km/h. The mean speed is
600 km/h during takeoff and landing. Use a
graphing strategy to estimate the amount of time
that the airplane travels at cruising speed.
6. Anya works as a senior sales rep for a computer
store. She earns $4500/month plus 5%
commission on her monthly sales, but she is
considering an offer of $3750/month plus 10%
commission from another store.
a) Which option is better if Anya’s monthly
sales average $12 000? Which option is
better for sales of $20 000?
b) Write equations for Anya’s two options, and
graph your equations.
c) How much in monthly sales would Anya
have to make for both options to have the
same value?
7. Five years ago, a high-school cafeteria charged
$5.85 for three pieces of fruit and a chicken
salad. Today, each piece of fruit costs 12%
more, while a chicken salad costs 15% more.
The new cost of three pieces of fruit and a
chicken salad is $6.66. Determine the new
prices of a piece of fruit and a chicken salad.
Lesson 1.3 Extra Practice | 7
Lesson 1.3 Extra Practice Answers
1. d)
5. 3 h 30 min
2. b)
6. a) Anya’s current job; the other offer
b) y = 4500 + 0.05x, y = 3750 + 0.10x
3. a)
b) (2, 1)
c) 3(2) – 1 = 5, 2 + 2(1) = 4
4.
c) $15 000
Copyright © 2011 by Nelson Education Ltd.
7. 84¢, $4.14
8 | Principles of Mathematics 10: Lesson 1.3 Extra Practice Answers
Chapter 1 Mid-Chapter Review Extra Practice
STUDENT BOOK PAGES 30–32
1. Define variables x and y for each situation, and
write an equation to represent the situation.
a) Indra earns $20/h at her day job and $12/h at
her evening job. Last month, she earned
$3600.
b) Laurent keeps a change jar for snack
machines. The jar contains $15.75 in loonies
and quarters.
c) Rebecca goes on a road trip, travelling at
100 km/h on six-lane highways and 80 km on
other highways. She travels a total distance
of 480 km.
2. Graph each equation for question 1.
3. Waterworld Rentals rents windsurfing boards
for $32/day and regular surfboards for $20/day.
Last Tuesday, Waterworld charged $960 for
rentals. Choose two strategies to represent the
possible combinations of windsurfing boards
and regular surfboards.
Copyright © 2011 by Nelson Education Ltd.
4. This graph shows the scale of fares charged by
Speedy Taxi Company.
a) What is the minimum fare for a Speedy
Taxi trip?
b) What is the fare for a 12 km trip?
c) How much extra does each kilometre cost?
d) Write an equation to represent Speedy Taxi
fares. Use your equation to determine the
fare for a 29 km trip.
5. A 1300 L water tank empties at the rate of
4 L/min. At 3:15 p.m., 170 L of the water is left
in the tank. Estimate when the tank was last
filled.
6. a) Graph the linear system 3x + 4y = 12 and
y = 2x – 3 by hand.
b) Estimate the solution to this system.
c) Check your answer for part b) using a
graphing calculator.
7. Elena runs an ice cream store. She sells a 1 L
tub of vanilla ice cream for $2.50 and a 1 L tub
of mocha ice cream for $3.30. She wants to
create a mix called Creamy Coffee Swirl to sell
for $3.00 per 1 L tub. How much of each
flavour must Elena use for one tub?
8. The equations y = 4, 2x + 3y = 8, and 2x – y = 8
form the sides of a triangle.
a) Graph the triangle, and determine the
coordinates of the vertices.
b) Calculate the area of the triangle.
Chapter 1 Mid-Chapter Review Extra Practice | 9
Chapter 1 Mid-Chapter Review Extra Practice Answers
1. a) Let x represent hours worked at the day
job, let y represent hours worked at the
evening job; 20x + 12y = 3600
b) Let x represent number of loonies, let y
represent number of quarters;
x + 0.25y = 15.75
c) Let x represent time driven on six-lane
highways, let y represent time driven on
other highways; 100x + 80y = 480
2. a)
3. Answers may vary, e.g.,
Let x represent
Graph:
the number of
windsurfing boards.
Let y represent
the number of
regular surfboards.
Equation:
32x + 20y = 960
Table of values:
x
0
5
10
15
20
25
30
y
48
40
32
24
16
8
0
Graphing calculator:
4. a) $4.50
b) $7.50
d) y = 0.25x + 4.50, $11.75
b)
c) 25¢
5. about 10:30 a.m.
b) about (2.2, 1.4)
c)
c)
7. 0.375 L of vanilla and 0.625 L of mocha
b) 16 square units
8. a)
(–2, 4), (4, 0), (6, 4)
10 | Principles of Mathematics 10: Chapter 1 Mid-Chapter Review Extra Practice Answers
Copyright © 2011 by Nelson Education Ltd.
6. a)
Lesson 1.4 Extra Practice
STUDENT BOOK PAGES 33–40
1. Isolate the indicated variable in each equation.
a) 3x + y = 7, y
c) 4x + 3y = 12, x
b) y – 3x + 2 = 0, x
d) 20x – 4y = 10, y
5. The difference between two adjacent angles in a
parallelogram is 42°. Determine the measures of
all four angles in the parallelogram.
2. Solve the linear system x + y = 5 and
3x – 2y = 25.
6. Without graphing, determine the intersection
point of the line 2x + y = 8 and the line passing
through (0, 6) and (9, 0).
3. A hat maker at a fair sells two kinds of novelty
hats. The banana-split hat sells for $3.50, and
the chocolate-sundae hat sells for $4.25. At the
end of the day, the hat maker has sold 76 hats
and taken in $290 in revenue. How many
chocolate-sundae hats were sold?
7. A change jar contains $7.55 in nickels, dimes,
and quarters. There are eight more nickels and
dimes than quarters, and 50 coins altogether.
How many of each coin are in the jar?
Copyright © 2011 by Nelson Education Ltd.
4. The hat maker in question 3 has to pay $130/day
to rent the stall at the fair, and the materials to
make each hat cost $2.25. Determine how many
hats per day the hat maker must sell to break
even if
a) only banana-split hats are sold
b) only chocolate-sundae hats are sold
Lesson 1.4 Extra Practice | 11
Lesson 1.4 Extra Practice Answers
1. a) y = 7 – 3x
1
2
b) x = y +
3
3
3
c) x = 3 – y
4
d) y = 5x – 2.5
2. (7, –2)
3. 32
4. a) 104
b) 65
5. 111°, 69°, 111°, 69°
6. (1.5, 5)
Copyright © 2011 by Nelson Education Ltd.
7. 12 nickels, 17 dimes, 21 quarters
12 | Principles of Mathematics 10: Lesson 1.4 Extra Practice Answers
Lesson 1.5 Extra Practice
STUDENT BOOK PAGES 41–48
1. a) Add and subtract the equations in the linear
system 5x – 3y = 6 and x + 2y = –4.
b) By graphing, verify that the two new
equations have the same solution as the
original linear system.
2. a) Multiply 3x – y = 5 by –2, and multiply
1
2x + 4y = 7 by .
2
b) Make a prediction about the graphs of the
two new equations, compared with the
graphs of the original two equations.
c) Suggest and apply a strategy to check your
prediction without graphing.
3. a) Multiply x + 3y = 5 by 2, and multiply
3x + 2y = 15 by 3.
b) Create another linear system by adding and
subtracting your equations for part a).
c) By graphing, verify that your linear system
for part b) is equivalent to the original linear
system for part a).
5. A student committee sells 104 tickets for a
concert. Student tickets cost $9, and non-student
tickets cost $12.50. The total revenue from
ticket sales is $1135.50.
a) Write two equations for this situation: one
equation describing the number of tickets
sold, and the other equation describing the
revenue.
b) Multiply your equation for the number of
tickets by 9. Then subtract this new equation
from your revenue equation. How are your
two new equations related to your equations
for part a)?
c) Determine the number of student tickets that
were sold. Explain your strategy.
6. a) Use a substitution strategy to solve the
system y + 5x + 32 = 0 and 3y – 4x = 37.
b) Show that multiplying the first equation by 3
and then adding and subtracting the
equations forms an equivalent system.
Copyright © 2011 by Nelson Education Ltd.
4. The linear system 2x – 3y = 2 and 3y – x = 8 is
equivalent to the linear system ax + 13y = –22
and 3x + by = –6. Determine the values of a
and b.
Lesson 1.5 Extra Practice | 13
Lesson 1.5 Extra Practice Answers
1. a) adding: 6x – y = 2;
subtracting: 4x – 5y = 10
b)
2. a) –6x + 2y = –10, x + 2y = 3.5
b) The graph of –6x + 2y = –10 will be the
same as the graph of 3x – y = 5; the graph
of x + 2y = 3.5 will be the same as the
graph of 2x + 4y = 7.
c) Answers may vary, e.g., check intercepts:
–6x + 2y = –10 and 3x – y = 5 both have
⎛5 ⎞
intercepts ⎜ , 0 ⎟ and (0, –5); x + 2y = 3.5
⎝3 ⎠
and 2x + 4y = 7 both have intercepts
(3.5, 0) and (0, 1.75).
4. a = –10, b = –6
5. a) x + y = 104, 9.00x + 12.50y = 1135.50
b) 9x + 9y = 936, 3.50y = 199.50; equivalent
to equations for part a)
c) 47; answers may vary, e.g., I solved the
equation 3.50y = 199.50 to determine that
y = 57, substituted this value into the
equation x + y = 104, and solved for x.
6. a) (–7, 3)
b) 6y + 11x = –59, 19x = –133; the solution is
again (–7, 3), so the systems are
equivalent.
Copyright © 2011 by Nelson Education Ltd.
3. a) 2x + 6y = 10, 9x + 6y = 45
b) adding: 11x + 12y = 55;
subtracting: –7x = –35
c)
14 | Principles of Mathematics 10: Lesson 1.5 Extra Practice Answers
Lesson 1.6 Extra Practice
STUDENT BOOK PAGES 49–56
1. For an Open House at a high school, a
student-run stall is selling two types of juice
drinks: Power Juice and Juice Cooler. The table
shows the amounts of pure juice and water in
each type.
Amount of
Juice (mL)
Amount of
Water (mL)
Power Juice
350
150
Juice Cooler
250
750
Type of Drink
If the students have 5.5 L of juice and 7.5 L of
water, how much of each type of drink can they
make?
Copyright © 2011 by Nelson Education Ltd.
2. During her morning commute, Rebecca
averaged 30 km/h in heavy city traffic and
90 km/h once she got onto the highway. She
travelled 35 km in 30 min. How far did Rebecca
drive while on the highway?
3. To eliminate x from each linear system, by what
numbers would you multiply equations ① and
②?
a) 2x – 3y = –1 ①
c) 5x + y = 12 ①
4x + y = 9 ②
–2x – 3y = 0 ②
b) 7x – 5y = 8 ①
d) 2x + 2y = 5 ①
y + 3x = 9 ②
3x – 2y = –3 ②
4. A linear system consists of the equations
3x – 2y + 10 = 0 and 5x + 4y = –13.
a) Solve the system by eliminating x.
b) Solve the system by eliminating y.
5. You need to solve the linear system 3x – 5y = 41
and 2y – 3x = –29.
a) Explain which variable you would choose to
eliminate.
b) Solve the system by eliminating the variable
you chose.
6. A local charity decides to invest $20 000 in two
funds. After one year, the returns on the funds
are 4% and 6%. If the total return on the
charity’s investment is $1040, how much did
the charity invest in the fund returning 4%?
7. Kara thinks of two numbers. She performs the
following steps:
Step 1: She doubles the first number and
subtracts three times the second number. The
result is 19.
Step 2: She switches the numbers and repeats
step 1. The result is –41.
Use an elimination strategy to discover Kara’s
two numbers.
Lesson 1.6 Extra Practice | 15
Lesson 1.6 Extra Practice Answers
1. 5 L of Power Juice, 8 L of Juice Cooler
2. 30 km
3. a) 2 and 1
b) 3 and 7
c) 2 and 5
d) 3 and 2
4. a), b) (–3, 0.5)
5. a) I would eliminate x because I don’t need to
multiply either equation by a number. I can
just add the equations.
b) (7, –4)
6. $8000
Copyright © 2011 by Nelson Education Ltd.
7. 17, 5
16 | Principles of Mathematics 10: Lesson 1.6 Extra Practice Answers
Chapter 1 Review Extra Practice
STUDENT BOOK PAGES 60–63
1. Steve has a budget of $25 each month to spend
on cell-phone calls and text messages. He pays
15¢/min for airtime and 25¢ per text message.
a) Use a table to show Steve’s possible
combinations of calls and text messages in
one month.
b) Draw a graph to represent Steve’s possible
combinations.
2. Carly buys a bulk lot of stuffed animals and
resells them at the school fair. The graph shows
Carly’s net profit or loss.
a) 3x + y = 1 and 2x – 5y = 6
b) x + 3y = 1 and x – 2y = 3
c) 3x + y = 1 and 5y – 2x = 6
d) x + 3y = 1 and 2x – 5y = 6
4. a) Isolate y in both equations in the system
4y + 7x = 19 and 5x – 2y = 13.
b) Use graphing technology to solve the system,
expressing your answers to the nearest
hundredth.
5. A transversal crosses
two parallel lines,
creating angles that
measure a and b as
shown. Determine a
and b if tripling the
angle measure a creates the same measure as
doubling the angle measure b.
Copyright © 2011 by Nelson Education Ltd.
6. Which linear system is not equivalent to the
system y – 2x = 13 and x + 5y = 10?
a) x – y = –8 and 3x + 2y = –9
b) 4x – 7y = 41 and y = 3
c) x = –5 and 3x + 5y = 0
d) x – y = –8 and x + y = –2
a) Estimate Carly’s profit or loss if she sells
37 stuffed animals.
b) Use the graph to write an equation that
represents Carly’s profit or loss.
c) Determine Carly’s exact profit or loss if she
sells 37 stuffed animals.
3. Which system of equations matches the graph
shown?
7. Jamal wants to make a 300 g serving of kiwi
and blueberries that contains 75 mg of
vitamin C. He knows that 1 g of kiwi contains
0.7 mg of vitamin C, and each gram of
blueberries contains 0.1 mg of vitamin C. Use
any appropriate strategy to determine how much
of each type of fruit Jamal should include.
8. a) Solve the system 3x + 2y = –4 and
5x – 2y = 12 using a substitution strategy.
b) Use an elimination strategy to solve the same
linear system.
c) Which strategy is more efficient for solving
this system? Explain in terms of both
strategies.
9. a) Given the equation 5y – 3x = 15, write
another equation to create a linear system
with each number of solutions.
i) none ii) one iii) infinitely many
b) Verify your answers for part a) graphically.
Chapter 1 Review Extra Practice | 17
Chapter 1 Review Extra Practice Answers
1. a)
b)
Calls
Number of
Minutes
Text Messages
Cost ($)
Number of
Messages
Cost ($)
Total
Cost ($)
0
0
100
25
25
20
3
88
22
25
40
6
76
19
25
60
9
64
16
25
80
12
52
13
25
100
15
40
10
25
120
18
28
7
25
140
21
16
4
25
160
24
4
1
25
2. a) loss of about $64 or $65
b) y = 4.75x – 240
c) loss of $64.25
3. a)
4. a) y =
9. Answers may vary, e.g.,
a) i) 5y – 3x = 10
iii) 10y – 6x = 30
ii) y – 3x = 9
b)
5
13
19 7
− x, y = x−
2
2
4 4
(2.65, 0.12)
5. a = 72°, b = 108°
6. b)
7. 75 g kiwi, 225 g blueberries
8. a), b) (1, –3.5)
c) Elimination is more efficient because the two
equations can simply be added together. For
substitution, isolating either variable involves
dividing both sides of one of the equations by
a number.
18 | Principles of Mathematics 10: Chapter 1 Review Extra Practice Answers
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b)