Chapter 7 Review
____
1. Which graph represents the following system of equations?
y = 3x + 3
y = –x – 3
a.
c.
b.
d.
2. By what number should you multiply the first equation to solve using elimination?
–3x – 2y = 2
–9x + 3y = 24
3. 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.
4. Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 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.
5. 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 number of nickels and dimes that are in the jar.
6. 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.
7-9 Graph each system. Tell whether the system has no solution, one solution, or infinitely many
solutions.
7. y = 5x – 4
y = 5x – 5
8. y = x + 4
y–4=x
9. y = 2x – 3
y = –x + 3
Solve the system of equations using any method.
10. y = 2x + 3
y = 3x + 1
11. 3x + 2y = 7
y = –3x + 11
12. 3x – 4y = –24
y + x = –1
13. 3x – y = 28
3x + y = 14
14. 3x – 4y = 9
–3x + 2y = 9
15. Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. There were 240 tickets sold for
a total of $1,155.00.
a.
Write a system of equations to model the situation.
b.
Solve the system to find the number of adult tickets sold and the number of student
tickets sold.
c.
Explain the method you used to solve the system.
Chapter 7 Review
Answer Section
1. ANS: D
2. ANS: 3
3. ANS:
y = −x + 0.90
y = −2x + 1.50
$.60 per egg, $.30 for toast
4. ANS:
y = x + 30
y = 5x + 18
3 months
5. ANS: 31 nickels and 29 dimes
6. ANS: 4 five-dollar bills, 10 one-dollar bills
7. ANS: no solutions
8. ANS: infinitely many solutions
9. ANS: one solution
10. ANS: (2, 7)
11. ANS: (5, –4)
12. ANS: (–4, 3)
13. ANS: (7, –7)
14. ANS: (–9, –9)
15. ANS:
a.
b.
c.
6a + 4.5s = 1,155
a + s = 240
There were 50 adult tickets and 190 student tickets.
Methods may vary. Sample: By multiplying the second equation by 6, it becomes 6a +
6s = 1,440. You can then use subtraction to eliminate a.