Name: _______________________________________ Block: _________
Systems of Equations and Inequalities Review
1. Find the solution of the system.
2. Solve the system by graphing.
(-4, 3)
(-3, 1)
Directions: Graph each system of inequalities. Shade appropriately.
3.
4.
5. Consider the system you graphed in question number three.
Are the points (0, 0), (0,4) and (1, 2) solutions to system? Explain your answer.
(0, 0) is a solution because it is in the shaded region of the graph which indicates
that the point makes both inequalities true.
(0, 4) is not a solution because it lies on a dotted line. This point does not make
the second inequality true.
(1, 2) is a solution because it lies on a solid line. This point makes both
inequalities true.
Name: _______________________________________ Block: _________
Directions: Solve using substitution.
6. y = -5x – 17
-3x – 3y = 3
7. 5x + y = 9 so y = -5x + 9
10x – 7y = -18
-3x – 3(-5x – 17) = 3
-3x + 15x + 51 = 3
12x + 51 = 3
12x = -48
x = -4
10x – 7(-5x + 9) = -18
10x + 35x – 63 = -18
45x – 63 = -18
45x = 45
x=1
y = -5(-4) – 17
y = 20-17 = 3
y = -5(1) + 9
y = -5 + 9 = 4
(-4, 3)
8. x = 9y +
7x – 1 = 63y
7(9y + 1/7) – 1 = 63y
63y + 1 – 1 = 63y
63 y = 63y
Infinite # of Solutions
(1, 4)
Directions: Solve using elimination.
9. (7x + 2y = 24) • -1
8x + 2y = 30
-7x – 2y = -24
x+0 =6
so x = 6
7(6) + 2y = 24
42 + 2y = 24
2y = -18
y = -9
10. -3x + 3y = 4
(-x + y = 3) • -3
3x – 3y = -9
0 + 0 = -5
No Solution
11. (12x – 7y = 1) • 4
(-5x + 4y = 5) • 7
48x – 28y = 4
-35x + 28y = 35
13x + 0 = 39
x
=3
-5(3) + 4y = 5
-15 + 4y = 5
4y = 20
y=5
(6, -9)
(3, 5)
Write and solve a system of equations for each of the word problems below.
Show both the equations and the work!
12. The difference in price in colored pencils and mechanical pencils is $0.20. If I
purchased 18 colored pencils and 22 mechanical pencils for $27.60, what is the cost
of the mechanical pencils?
18c + 22m = 27.60
c – m = .20
+m +m
so c = .20 + m
Substitution: 18(.20 + m) + 22m = 27.60
3.6 + 18m + 22m = 27.60
3.6 + 40m = 27.60
40m = 24
m = .60
c = .20 + (.60)
c = .80
Mechanical Pencils are $0.60.
Colored Pencils are $0.80.
Name: _______________________________________ Block: _________
13. Blake buys paperback books from the used book store for $5 each. Natalie
purchased an annual membership to the same bookstore for $35 so she can buy
paperbacks at a discounted price of $2.50 each. How many books would Natalie
and Blake have to buy this year for their spending at the bookstore to be the same?
What would their total cost be?
Blake:
Natalie:
s = 5b
s = 2.5b + 35
Substitution: 5b = 2.5b + 35
2.5b = 35
b = 14
s = 5(14)
s = 70
Natalie and Blake with both spend $70 if they buy 14 books.
14. Mr. Duellman has a total of 26 dimes and quarters in his desk drawer, totaling
$3.65. How many of each type of coin does he have?
(d + q = 26) • - .1
.1d + .25q = 3.65
Elimination: -.1d - .1q = -2.6
.1d + .25q = 3.65
0 + .15q = 1.05
q=7
d + 7 = 26
d = 19
7 quarters and 19 dimes.
15. The Kendall family was preparing to go hiking with the Dudly family. In preparation,
the Kendall’s bought 8 Cliff Bars and 4 apples for $12.40. The Dudly family spent
$24.30 on 15 Cliff Bars and 9 apples. How much was each cliff bar and each apple?
(8c + 4a = 12.40) • -9
(15c + 9a = 24.30) • 4
Elimination: -72c – 36a = -111.60
60c + 36a = 97.20
-12c + 0 = -14.40
c
= 1.20
8(1.20) + 4a = 12.40
9.60 + 4a = 12.40
4a = 2.80
a = .70
Cliff Bars are $1.20 and apples are $0.70.
16. Piglet and Tigger are having a reading contest to see who can read the most books
this year. Piglet has already read sixteen books, and she plans to read two books
every week for the rest of the year. Tigger has only read four books, but he plans to
28
catch up by reading four books per week.
a. Write a system of equations to represent
this situation.
Piglet: T = 16 + 2w
Tigger: T = 4 + 4w
b. Solve the system from part (a) by graphing.
Will Tigger ever catch up to Piglet?
If so, when? How many books will this be?
Hint: You may need to count
by 2’s on the y-axis.
#
of
B
o
24
20
16
o
12
k
8
s
4
(6, 28)
After 6 weeks they will have both read 28 books.
# of Weeks
0
0 1 2 3 4 5 6 7 8 9 10