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Chapter 7 - Systems of Equations

Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.

1.

Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding  CD a month to his collection while Nita is adding 5 CDs a month to her collection. Write and graph a system to find the number of months after which they will have the same number of CDs. Let x represent the number of months and y the number of CDs.
 a.   3 months c.   1 month b.   2 months d.   33 months

2.

Kendra owns a restaurant. She charges \$1.50 for 2 eggs and one piece of toast, and \$.90 for one egg and one piece of toast. Write and graph a system of equations to determine how much she charges for each egg and each piece of toast. Let x represent the number of eggs and y the number of pieces of toast.
 a.   \$.60 per egg, \$.30 for toast c.   \$.30 per egg, \$.60 for toast b.   \$.30 per egg, \$.60 for toast d.   \$.60 per egg, \$.30 for toast

3.

Find the value of b that makes the system of equations have the solution (3, 5).
y = 3x – 4
y = bx + 2
 a. 0 b. –1 c. 2 d. 1

Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

4.

y = x + 4
y – 4 = x
 a. infinitely many solutions b. no solutions c. one solution

5.

y = 2x – 3
y = –x + 3
 a. one solution b. no solutions c. infinitely many solutions

6.

y = 5x – 4
y = 5x – 5
 a. no solutions b. one solution c. infinitely many solutions

7.

Use substitution to solve the following system of equations.
d + ef = 11
e = f + d + 5
f = 2e – 12
 a. d = 3, e = 4, f = –4 c. d = 4, e = 3, f = –4 b. d = 3, e = 4, f = –4 d. d = –4, e = 4, f = 3

8.

The length of a rectangle is 2 cm more than four times the width. If the perimeter of the rectangle is 84 cm, what are its dimensions?
 a. length = 8 cm; width = 34 cm c. length = 30 cm; width = 10 cm b. length = 34 cm; width = 8 cm d. length = 34 cm; width = 10 cm

Solve the system of equations using substitution.

9.

y = 2x + 3
y = 3x + 1
 a. (–2, –1) b. (–1, –2) c. (2, 7) d. (–2, –5)

10.

y = 2x – 10
y = 4x – 8
 a. (3, 4) b. (–1, –12) c. (–4, –17) d. (3, –4)

11.

3y = – x + 2
y = –x + 9
 a. (3, 6) b. (20, –4) c. (10, –1) d. (–1, 8)

12.

y = 4x + 6
y = 2x
 a. (–3, –6) b. (3, 6) c. (6, 3) d. (1, 2)

13.

3x + 2y = 7
y = –3x + 11
 a. (6, –3) b. (6, –7) c. d. (5, –4)

14.

y = x + 6
y = –2x – 3
 a. (1, 7) b. (–3, 3) c. d. (4, –11)

15.

Sharon has some one-dollar bills and some five-dollar bills. She has 14 bills. The value of the bills is \$30. Solve a system of equations using elimination to find how many of each kind of bill she has.
 a. 4 five-dollar bills, 10 one-dollar bills c. 5 five-dollar bills, 5 one-dollar bills b. 3 five-dollar bills, 10 one-dollar bills d. 5 five-dollar bills, 9 one-dollar bills

Solve the system using elimination.

16.

6x + 3y = –12
6x + 2y = –4
 a. (10, –16) b. (2, –8) c. (–2, 8) d. (–10, 16)

17.

3x + y = 11
4xy = 17
 a. (–1, 4) b. (4, –1) c. (5, –4) d. (1, 4)

18.

–10x – 3y = –18
–7x – 8y = 11
 a. (–7, –10) b. (–4, 3) c. (3, –4) d. (2, –1)

19.

5x = –25 + 5y
10y = 42 + 2x
 a. (–1, 2) b. (–1, 4) c. (4, –1) d. (5, 10)

20.

3xy = 28
3x + y = 14
 a. (8, –4) b. (–7, 7) c. (7, –7) d. (–4, 8)

21.

By what number should you multiply the first equation to solve using elimination?
–3x – 2y = 2
–9x + 3y = 24
 a. 6 b. –9 c. –3 d. 3

22.

A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is \$4.45. Solve by elimination to find the amount of nickels and dimes that are in the jar.
 a. 30 nickels and 28 dimes c. 29 nickels and 31 dimes b. 31 nickels and 29 dimes d. 30 nickels and 32 dimes

23.

You decide to market your own custom computer software. You must invest \$3,255 for computer hardware, and spend \$2.90 to buy and package each disk. If each program sells for \$13.75, how many copies must you sell to break even?
 a. 196 copies b. 301 copies c. 300 copies d. 195 copies

24.

An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged \$32.00. Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was charged \$35.25. What is the admission fee? What is the rental fee for a pair of skates?
 a. admission fee: \$3.25skate rental fee: \$2.50 c. admission fee: \$3.00skate rental fee: \$2.00 b. admission fee: \$3.50skate rental fee: \$3.00 d. admission fee: \$4.00skate rental fee: \$3.50

25.

Mike and Kim invest \$14,000 in equipment to print yearbooks for schools. Each yearbook costs \$7 to print and sells for \$35. How many yearbooks must they sell before their business breaks even?
 a. 650 b. 2,000 c. 500 d. 400

26.

At the local ballpark, the team charges \$5 for each ticket and expects to make \$1,400 in concessions. The team must pay its players \$2,000 and pay all other workers \$1,600. Each fan gets a free bat that costs the team \$3 per bat. How many tickets must be sold to break even?
 a. 440 b. 1,100 c. 2,500 d. 275