Substitute and Evaluate 1. Evaluate each expression when x = 4 and
y = −3. a) 2x + 4y b) −3x − 2y
c) − 4x + 3y + 5 d) 1 22 3
x y−
2. Evaluate each expression when a = −1 and b = 2. a) a − b + 4 b) −3a + 2b − 7
c) 34
a b− d) 2 13 3
b a−
Simplify Expressions 3. Simplify.
a) 3x + 2(x + y) b) 4x − 3(x − y) c) 3a − 4b + 6a − 2b d) − 4a − 3b − (2a + 5b)
4. Simplify. a) a − 2(2a + 3b) − 4(4a − b) b) 3(x + y) − 2(x − 3y) + 6(2x + y) c) 4(3x − y) − 6(x + 2y) − 5(x − 6) d) 3(a + b + c) − 2(3a + 2b − c)
Graph Lines 5. Graph each line. Use a table of values or
the slope and y-intercept method.
a) y = −3x + 2 b) 1= 43
y x −
c) 1= 32
y x + d) 2= 25
y x− −
6. Graph each line by first rewriting the equation in the form y = mx + b. a) x + y + 3 = 0 b) 3x − 2y + 6 = 0 c) −2x + 3y − 18 = 0
d) 1 1 2 = 02 3
x y− + +
7. Graph each line by finding the intercepts. a) x − y = 4 b) 3x + 2y = 12 c) − 4x + 3y = 24 d) 7x − 2y = 14
8. Graph each line. Choose a convenient method.
a) 2= 43
y x + b) 2x − 5y = 10
c) x + y = 3 d) y = −5x + 4 Use a Graphing Calculator to Graph a Line 9. Graph each line in question 5 using a
graphing calculator.
10. Use your rewritten equations from question 6 to graph each line using a graphing calculator.
Percent 11. Calculate each amount.
a) the amount of sugar in 200 g of a 14% sugar IV drip
b) the amount of interest owed at the end of a month on an outstanding balance of $3500 on a credit card if the company charges 1.5% per month
12. Find the simple interest earned after 1 year on each investment. a) $3000 invested at 2% per year b) $15 000 invested at 6% per year c) $9200 invested at 4.2% per year d) $13 500 invested at 3.7% per year
Use a Computer Algebra System (CAS) to Evaluate Expressions 13. Evaluate.
a) 4x + 2 when x = 0 b) 5y − 7 when y = 2 c) −3z + 6 when z = −1
14. Use a CAS to check your answers in question 1. Hint: First substitute x = 4, and then substitute y = −3 in the resulting expression.
Use a CAS to Rearrange Equations 15. Use a CAS to check your work in question 6.
1. 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 2. 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
3. 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, 355 tickets were sold.
There were 51 more student tickets sold than adult tickets.
b) A rectangle has a perimeter of 172 cm. The length of the rectangle is 23 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 113.
d) Enrico weighs 7 kg more than Julian. The sum of their masses is 183 kg.
5. Find the point of intersection for each pair of lines. Check your answers. a) y = 3x + 10 b) y = x − 1 y = 4x + 7 y = 9 − x c) y = x + 3 d) y = 1 − 2x y = 1 − x y = x − 5
6. Find the point of intersection for each pair of
lines. Check your answers. a) x − y = 4 b) 3x − 3y = −3 3x + y = 24 2x + y = 4 c) x + y = 4 d) 5x − 2y = 10 2x + 3y = 9 x + 2y = 2
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) 2x + 5y = −20 b) 3x + 2y = 3 5x − 3y = −15 2x + 10y = −5 c) 2x + 3y − 7 = 0 d) y = − 0.5x − 1 3x − 5y − 13 = 0 y = 0.25x + 1
8. Charlene is looking into cell phone plans. Cell Plus gives unlimited minutes for $50/month. A1 Cell offers a $40 monthly fee, plus 5¢/min for any time over 300 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 10 h per month? 6 h per month?
1. Solve each linear system using the method of substitution. Check your answers. a) y = 2x − 3 x + y = 6 b) x = − 4y − 6 2x + 6y = 5 c) 2x + y = 6 3x + 2y = 10 d) 5 = 2y − x 7 = 3y − 2x
2. 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) 3x + 2y = 6 x + 6y = 5 b) 2x + y = 7 3x + 4y = 5 c) −x + 3y = 4 3x + 2y = 5 d) 3x − 4y = 6 x − y = 11
3. Is (2, −3) the solution for the following linear
system? Explain how you can tell. 3x + 6y = −12 2y − 8x = −22
4. Solve by substitution. Check your solution.
a) 3x = y + 3 2x + 3y = 13 b) 4x − y = −9 3y − 2x = 17 c) 2c − d + 2 = 0 3c + 2d + 10 = 0 d) 4x + y = 0 x + 2y + 1 = 0
5. Simplify each equation, and then solve the linear system by substitution. a) 3(x + 1) − 2(y − 2) = − 6 x + 4(y + 3) = 29 b) 2(x − 1) − 3(y − 3) = 0 3(x + 2) − (y − 7) = 20 c) 2(3x − 1) − (y + 4) = 7 4(1 − 2x) − 3(3 − y) = −12 d) 2(x − 1) − 4(2y + 1) = −1 x + 3(3y + 2) = 2
6. The number of tickets sold for a school event
is 330. 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 $10. In total, $2380 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 $200 initiation
fee, plus $15 per month. Champion Health Club charges a $100 initiation fee, plus $20 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 1 year, which
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 = 10 3a − 2b = 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 $34. Five veggie subs and six roast beef subs cost $61. Write and solve a system of equations to find the cost of each type of sub.
9. A weekend at Skyview Lodge costs $360
and includes two nights’ accommodation and four meals. A week costs $1200 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.
10. The Mackenzie, the longest river in Canada,
is 1056 km longer than the Yukon, the second-longest river. The total length of the two rivers is 7426 km. Find the length of each river.
1. The sum of two numbers is 56. One number exceeds the other number by 2. Find the two numbers.
2. Three soccer balls and a basketball cost
$155. Two soccer balls and three basketballs cost $220. Find the cost of each ball.
3. The students in the school band are selling
chocolate-covered almonds for $3 a box and chocolate bars for $2 each to raise money for a band trip. Mary sold a total of 96 items and raised $233. 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 $250 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 175 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 11% per year. The interest paid after 1 year on the 11% investment is $212 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 38 h worked in a week. One week, Monique worked 45 h and was paid $833. In the same week, Henri worked 40 h and was paid $713. 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 1-day rental and 240 km driven is $39. The cost for a 5-day rental and 900 km driven is $165. Find the cost per day and the cost per kilometre.
8. One type of granola is 30% fruit, and another
type is 15% fruit. What mass of each type of granola should be mixed to make 600 g of granola that is 21% fruit?
9. What volume, in millilitres, of a 60%
hydrochloric acid solution must be added to 100 mL of a 30% hydrochloric acid solution to make a 36% hydrochloric acid solution?
10. Playing tennis burns energy at a rate of about
25 kJ/min. Cycling burns energy at about 35 kJ/min. Hans exercised by playing tennis and then cycling. He exercised for 50 min altogether and used a total of 1450 kJ of energy. For how long did he play tennis?
11. Erika drove from Ottawa at 80 km/h. Julie
left Ottawa 1 h later and drove along the same road at 100 km/h. How far from Ottawa did Julie overtake Erika?
12. A street has a row of 15 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 $3000 more than the first house, the third house costs $3000 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 $3 091 000. What is the selling price of the house at each end of the street? Explain and justify your reasoning.
1.1 Connect English With Mathematics and Graphing Lines 1. 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 $25. c) Three times Jennifer’s age is 26 more
than Herbert’s age. 2. Write a system of equations for each
situation. a) Michael is three times older than his sister
Angela. In 1 year, Michael will be twice as old as Angela. How old are the two children today?
b) A $2 raffle ticket offers a bonus $1 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 $2 and how many were bought for $3? 3. Graph each pair of lines to find their point of
intersection. a) y = x − 5 y = 3 − x b) y = 3x + 8 x + 2y = 2 c) 2x − y = − 4 2x + y = 6 d) 3x − 2y = −8 x − 2y = − 4
1.2 The Method of Substitution 4. Solve each linear system using the method of
substitution. a) 2x + y = 7 3x − 2y = 21 b) y = 2x + 4 x − 4y = −9
c) 3s + 5t = 2 s + 4t = − 4 d) 3m − 6n = 1 m + 3n = 2
5. Is the point (3, 5) the solution to each system
of linear equations? Explain. a) 2x − y = 1 3x + 4y = 29 b) x + y = 8 2x − y = −1
6. The two largest deserts in the world are the
Sahara Desert and the Australian Desert. The sum of their areas is 13 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.
1.3 Investigate Equivalent Linear Relations and Equivalent Linear Systems 7. Which of the following equations is
equivalent to 2 1=3 5
y x + ?
A y = 2x + 1 B 3y = 2x + 1 C 15y = 10x + 3 D 10x − 15y + 5 = 0
a) Explain why the following is an equivalent linear system.
x − 5y = 15 2x + 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 31. 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.
1.4 The Method of Elimination 10. Solve each linear system. Check each
solution. a) x − y = 14 2x + 5y = −7 b) 2x − 3y = − 4 3x + y = 5 c) 3x + 4y = 17 7x − 2y = 17 d) 2x + 5y = 18 3x + 5y − 17 = 0
12. Cindy buys a large pizza with two toppings for $13.50. 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.
1.5 Solve Problems Using Linear Systems 13. A chemist needs 10 L of 21% salt solution.
The chemist has two salt solutions available at 15% and 25% salt. Write and solve a linear system to find the volume of each solution that needs to be combined to make the mixture.
14. Flying into the wind, a plane takes 6 h to fly
3000 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?
15. The public golf course runs a junior league
with a registration fee of $200 and a cost of $25 per round played. To stay competitive, the private golf club in the same town offers a junior league with a registration fee of $250, but only $20 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 16 rounds in
the league. ii) Jacob plans to play 8 rounds in the
1. The equation 4x − 2y + 8 = 0 written in slope y-intercept form is A y = −2x + 4 B y = 2x − 4 C y = −2x − 4 D y = 2x + 4
2. An equation equivalent to 1 1=4 2
y x − is
A 4y = x − 1 B 2y = x − 2 C x − 4y − 2 = 0 D 2y + 4x = 4
3. 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 = 2x + 5 b) y = x − 1 3x − 5y = −11 y = 2x − 5 c) y = 4x + 4 d) x − y = 1 x + 5y = −1 3x + 2y = −12
5. Solve each linear system using substitution.
a) y = 2x − 1 b) 2x − y = −2 3x − 2y = − 4 x − 5y = 19 c) 2x + y = 6 d) x + 2y + 2 = 0 3x − 2y = 2 2x − 6y + 9 = 0
6. Solve each linear system using elimination.
a) x − y = 3 b) 4x + 5y = 14 x + 2y = 27 2x − 3y = −2 c) −2x + 5y = −3 d) 3x + 2y = 8 2x − 3y = 1 2x + 3y = 7
7. Solve each system by any method. Check
each solution. a) 5x − 3y = 9 b) 3a + b − 4 = 0 2x − 5y = − 4 2a − 10 = 3b c) 3p − 6q = 0 d) 2x + 3y = −2 4p + q = 3 8x + 5y = −6
8. Romano Pizza is selling a large pizza for $14 plus $1 per topping. A Slice of Italy Pizza is selling the same size pizza for $12 plus $1.50 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 22.
Twice the smaller number exceeds the larger number by 17. What are the two numbers?
10. A container has 30 bolts in it and has a mass
of 635 g. When an additional 15 bolts are placed in the container, the mass is 935 g. Find the mass of a bolt and the mass of the container.
11. Lawrence is 12 years older than Patrick. Last
year, he was twice as old as Patrick. How old is each person now?
12. White vinegar is a solution of acetic acid in
water. There are two strengths of white vinegar—a 5% solution and a 10% solution. How many millilitres of each solution must be mixed to make 50 mL of a 9% vinegar solution?
13. 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 $340 in interest. How much did he invest in each plan?
1. An equation for the line with slope −2 and y-intercept 4 is A 2x − y = 4 B x − y = 4 C x + 2y = 4 D 2x + y = 4
2. The point (1, −2) is the solution to which linear system? A 3x + 5y = 13 B x − y = 3 x + y = −1 2x + 4y = −6 C 3x − y = 5 D 5x + 3y = 1 2x + y = 1 3x + 5y = −7
3. 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) 2= 43
y x − b) x = 7.5
2= 25
y x −
c) 2x − 3y = 12 2x − 4y = 11
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 16. b) Two numbers add together to give 14 and
differ by 4. c) The perimeter of a rectangle is 22 cm.
The length is 3 cm more than the width. d) Erin earns twice as much as Michael every
week. Last week, their earnings added to $309.40.
5. Solve each linear system by graphing. a) y = 3x + 1 b) 4x + 3y = 7 2x − 3y = 11 4x − 3y = 1 c) 3x + y = 1 d) x + y = 4 x + 4y = 4 3x = 10 − 2y
6. Solve each linear system using substitution. a) y = x − 4 b) y = 2x − 9 2x + 5y = 1 x − y = 4 c) x − y = 5 d) 7 = b − 2a 3x + y = 3 4 = a + b
7. Solve each system using elimination. a) x + y = 4 b) 2x − 4y = −2 x − y = −8 3x + y = 4 c) 5x + 7y = 3 d) 3c + 2d = −12 2x + 3y = 1 2c + 3d = −13
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 2.5 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 25% almonds. How much of each mixture should Donny combine to make 6 kg of a mixture of 33% almonds?
11. a) 28 g b) $52.50 12. a) $60 b) $900 c) $386.40 d) $499.50 13. a) 2 b) 3 c) 9
Section 1.1 Practice Master
1. a) 3x + 6 b) 1 53 n −
c) (x + 4)y d) 14p −
2. a) 3l b) 0.15A
c) 12 d d) 0.11m
3. a) 3x − 4 = 2 b) 1 2 = 13 n +
c) x = 5(y + 2) d) 1.14x = 95.76 4. a) a + a + 51 = 355 b) 2(w + 2w + 23) = 172 c) 2x + 3(x + 1) = 113 d) j + j + 7 = 183 5. a) (3, 19) b) (5, 4) c) (−1, 2) d) (2, −3) 6. a) (7, 3) b) (1, 2) c) (3, 1) d) (2, 0) 7. a) (−4.35, −2.26) b) (1.54, −0.81) c) (3.89, −0.26) d) (−2.67, 0.33) 8. a) C = 50; C = 40 + 0.05t; C is the monthly charge and
t is time, in minutes, over 300 min/month b) (200, 50) c) Both plans cost $50 for 500 min/month
(300 min + 200 min). d) Cell Plus; A1 Cell
Section 1.2 Practice Master
1. a) (3, 3) b) ( )1728, 2
c) (2, 2) d) (1, 3) 2. a) Solve x + 6y = 5 for x; x = 5 − 6y. b) Solve 2x + y = 7 for y; y = 7 − 2x. c) Solve −x + 3y = 4 for x; x = 3y − 4. d) Solve x − y = 11 for x or y; x = 11 + y or y = x − 11. 3. Yes. The point satisfies both equations. 4. a) (2, 3) b) (−7, −19)
c) (−2, −2) d) ( )1 4,7 7−
5. a) ( )32 9,7 7− b) (4, 5)
c) (3.2, 6.2) d) ( )1 1,2 2−
6. a) a + s = 330; 6a + 10s = 2380 b) 230 adult tickets and 100 student tickets 7. a) C = 15t + 200; C = 20t + 100; C is the cost and t is
time, in minutes. b) (20, 500) c) 20 months d) Champion Health Club
Section 1.3 Practice Master 1. A and D 2. Answers may vary. For example: a) 2y = −8x + 6; 3y = −12x + 9 b) 6x + 4y = 10; 9x + 6y = 15 c) 4x + 10y − 12 = 0; − 4x − 10y + 12 = 0
d) 2y = 12x − 6; 332 2y x= −
3. Answers may vary. For example: 2(l + w) = 30; l + w = 15
4. Answers may vary. For example: 0.25q + 0.05n = 1.65; 5q + n = 33
5. Equation is equation multiplied by 3. 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 1.4 Practice Master 1. a) (5, 4) b) (2, 2) c) (−1, 3) d) (0, −3)
2. a) ( )1 3,2 2− − b) (9, 6)
c) (−1, −3) d) (5, 3) 3. a) (−2, −1) b) (0, −6) c) (1, −2) d) (1, 0) 4. a) (−1, −3) b) (1, 6) c) (−2, 3) d) (1, 3)
5. a) (1, 1) b) ( )52 57,11 11
c) (−1, −3) d) (−0.4, −1.1) 6. a) (12, 6) b) (2, 1)
7. a) There are 10 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. 2n + 4m = 360 7n + 10m = 1200 Solution: (150, 15) One night’s accommodation costs $150 and one meal
costs $15. 10. The Mackenzie is 4241 km long and the Yukon is
3185 km long.
Section 1.5 Practice Master 1. 27, 29 2. soccer ball $35, basketball $50 3. chocolate almonds 41, chocolate bars 55 4. a) C = 5p + 250; C = 4p + 400; C is the cost and p is
the number of pages. b) (150, 1000) c) Printing 150 pages costs $1000 at both companies. d) the second company 5. $2800 at 11%; $1200 at 8% 6. regular rate $17.50, overtime rate $24 7. $15/day; $0.10/km 8. 240 g of 30% fruit; 360 g of 15% fruit 9. 25 mL 10. 30 min 11. 500 km 12. 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 $200 000 and the house on the other end costs $186 000.
Chapter 1 Review 1. a) Let the middle number be x. x − 1 + x + x + 1 = 75 b) Let l represent the number of loonies and t
represent the number of toonies. l + 2t = 25 c) Let j represent Jennifer’s age and h represent
Herbert’s age. 3j = h + 26 2. a) m = 3a; m + 1 = 2(a + 1) b) x + y = 400; 2x + 3y = 894 3. a) (4, −1) b) (−2, 2)
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 16, Centreville 15 10. a) (9, −5) b) (1, 2) c) (3, 2) d) (−1, 4) 11. a) (3, − 4) b) (2, 2) 12. cost of a large pizza $12, cost per topping $0.75 13. 4 L of 15% salt and 6 L of 25% salt 14. plane speed 550 km/h, wind speed 50 km/h 15. a) C = 25r + 200; C = 20r + 250 b) (10, 450) c) It costs $450 for 10 rounds at both clubs. d) i) private club ii) public club
Chapter 1 Practice Test 1. D 2. C 3. a) R − 1 = 2(S − 1) b) l = 3w + 5
c) 3x − 2 = 11 d) 1 ( 10) = 142 a +
4. a) (−2, 1) b) (4, 3) c) (−1, 0) d) (−2, −3)
5. a) (6, 11) b) ( )29 40,9 9− −
c) (2, 2) d) ( )13, 2−
6. a) (11, 8) b) ( )16 18,11 11
c) (−1, −1) d) (2, 1) 7. a) (3, 2) b) (2, −2)
c) ( )2 1,3 3 d) ( )4 2,7 7− −
8. a) C = t + 14; C = 1.5t + 12; C is the cost and t is the number of toppings.
b) (4, 18) c) A four-topping large pizza costs $18 at both
places. d) Romano Pizza 9. 61, 39 10. bolt 20 g, container 35 g 11. Lawrence 25, Patrick 13 12. 10 mL of the 5% solution and 40 mL of the 10%
solution 13. $2000 at 5%/year and $3000 at 8%/year
Chapter 1 Test 1. D 2. B 3. 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 = 3a; j − 2 + a − 2 = 16 b) x + y = 14; x − y = 4 c) 2(l + w) = 22; l = w + 3 d) e = 2m; e + m = 309.40 5. a) (−2, −5) b) (1, 1) c) (0, 1) d) (2, 2) 6. a) (3, −1) b) (5, 1) c) (2, −3) d) (−1, 5) 7. a) (−2, 6) b) (1, 1) c) (2, −1) d) (−2, −3) 8. a) C = 40t + 70; C = 45t + 50 b)
c) Both companies charge $230 for a 4-h service call. d) KemiKal Balance 9. 3.2 kg of 40% almonds and 2.8 kg of 25% almonds
