unit 7 summative review · parallel 1 ©j i2g0q1y8d vkzugtgay csiotfhtvwnasrseg tlhldcr.y o zakl\lz...
TRANSCRIPT
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8th Grade Math
Unit 7 Summative Review
Name___________________________________
Date________________
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-1-
Solve each system by graphing.
1) y = -4x + 3
y = x - 2
x
y
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
(1, -1)
2) y = -2x + 3
y = 2x - 1
x
y
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
(1, 1)
3) y = -2
3x + 1
y = -2
3x - 1
x
y
-10 -8 -6 -4 -2 2 4 6 8 10
-10
-8
-6
-4
-2
2
4
6
8
10
No solution
4) y = -5
2x - 9
y = 2x + 9
x
y
-10 -8 -6 -4 -2 2 4 6 8 10
-10
-8
-6
-4
-2
2
4
6
8
10
(-4, 1)
KEY
-SLOPE : -2 YWTCO ,
3)→ SLOPE : -4 YWTCO,
3)
→ SLOPE : 2 YINT ( 0,
- D7 scope : I YWTCO
,- 2)
aslope : - £ YNTCO,- 9)
-SLOPE : - 23 YWT ( 0 ,D
→ slope : 2 YWT ( 0,9 )
→ slope : -25 Yint ( 0.
- D
1PARALLEL
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-2-
5) 2x + 40 = 10y
7x - 10 = 5y
x
y
-10 -8 -6 -4 -2 2 4 6 8 10
-10
-8
-6
-4
-2
2
4
6
8
10
(5, 5)
6) -y - 7 = 2x
4y = -4 - 2x
x
y
-10 -8 -6 -4 -2 2 4 6 8 10
-10
-8
-6
-4
-2
2
4
6
8
10
(-4, 1)
7) -3y + 4x + 15 = 0
0 = 3y - 15 - 4x
x
y
-10 -8 -6 -4 -2 2 4 6 8 10
-10
-8
-6
-4
-2
2
4
6
8
10
Infinite number of solutions
8) 0 = 7y - 4x - 21
8 + x = -y
x
y
-10 -8 -6 -4 -2 2 4 6 8 10
-10
-8
-6
-4
-2
2
4
6
8
10
(-7, -1)
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-scope ! - ¥
5- It '=#¥x
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-3-
Solve each system.
9) y = 2x + 7
y = -3x - 8
A) (3, 2) B) (-3, 4)
C) (-3, 1)* D) (-3, 2)
10) y = -4x - 10
y = 2x + 8
A) (1, -3) B) (-1, -3)
C) (-4, -3) D) (-3, 2)*
11) y = -3x
y = 4x - 7
A) (3, -1) B) No solution
C) (1, -3)* D) (3, 1)
12) y = -4x + 9
y = -3x + 6
A) (-3, 4) B) (2, 4)
C) (3, -3)* D) (-2, 4)
13) 2x + 3y = 1
6x - 3y = -9
A) (1, 1) B) (-1, 1)*
C) (-2, 1) D) (1, -1)
14) 2x - 3y = 6
-x + 3y = -9
A) (3, 4) B) (-4, -3)
C) (-3, -4)* D) (-6, 4)
15) DeShawn and Adam are selling fruit for a school fundraiser. Customers can buy small boxes of
grapefruit and large boxes of grapefruit. DeShawn sold 2 small boxes of grapefruit and 5 large
boxes of grapefruit for a total of $120. Adam sold 2 small boxes of grapefruit and 6 large boxes
of grapefruit for a total of $140. Find the cost each of one small box of grapefruit and one large
box of grapefruit.
*A) small box of grapefruit: $10, large box of grapefruit: $20
B) small box of grapefruit: $16, large box of grapefruit: $28
C) small box of grapefruit: $20, large box of grapefruit: $10
D) small box of grapefruit: $6, large box of grapefruit: $25
→CHECK ANSWERS BY PLUGWG IN X B Y !
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-4-
16) The school that Castel goes to is selling tickets to the annual talent show. On the first day of
ticket sales the school sold 3 adult tickets and 2 student tickets for a total of $30. The school
took in $26 on the second day by selling 2 adult tickets and 2 student tickets. What is the price
each of one adult ticket and one student ticket?
A) adult ticket: $6, student ticket: $8 B) adult ticket: $4, student ticket: $9*
C) adult ticket: $3, student ticket: $12 D) adult ticket: $5, student ticket: $6
Solve each system by substitution.
17) y = 3
y = x + 6
(-3, 3)
18) y = 4x + 12
y = -2x
(-2, 4)
19) y = x + 7
-2x + 3y = 15
(-6, 1)
20) -3x - 4y = 9
y = 2x - 5
(1, -3)
21) 10x + 2y = -7
5x + y = 2
No solution
22) -4x - 8y = -24
-x + y = -3
(4, 1)
23) 7x - y = -15
-2x - 2y = 18
(-3, -6)
24) 14x - 6y = -4
7x - 3y = -2
Infinite number of solutions
f 3=xt6- 6
: =x
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-5-
Solve each system by elimination.
25) 2x - 5y = -10
-2x + 3y = 2
(5, 4)
26) -x - 4y = -10
-x + 4y = 6
(2, 2)
27) 7x + 6y = -22
-2x + y = 28
(-10, 8)
28) 4x - 10y = -10
-x - 2y = 16
(-10, -3)
29) 6x + 5y = -10
3x - y = 23
(5, -8)
30) -2x - 5y = 0
-4x + 3y = 0
(0, 0)
31) -2x - 7y = 10
3x + 4y = -15
(-5, 0)
32) 7x + 3y = -24
3x - 2y = -30
(-6, 6)
33) The sum of two numbers is 18. Their difference is 4. Find the numbers.
7 and 11
34) Find the value of two numbers if their sum is 20 and their difference is 4.
8 and 12
35) The difference of two numbers is 3. Their sum is 17. Find the numbers.
7 and 10
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-6-
36) The sum of two numbers is 19. Their difference is 5. What are the numbers?
7 and 12
37) The school that Julia goes to is selling tickets to a play. On the first day of ticket sales the school
sold 1 senior citizen ticket and 5 student tickets for a total of $33. The school took in $21 on the
second day by selling 1 senior citizen ticket and 3 student tickets. What is the price each of one
senior citizen ticket and one student ticket?
senior citizen ticket: $3, student ticket: $6
38) Chelsea and Nicole are selling cookie dough for a school fundraiser. Customers can buy
packages of sugar cookie dough and packages of double chocolate cookie dough. Chelsea sold 5
packages of sugar cookie dough and 4 packages of double chocolate cookie dough for a total of
$105. Nicole sold 4 packages of sugar cookie dough and 4 packages of double chocolate cookie
dough for a total of $100. What is the cost each of one package of sugar cookie dough and one
package of double chocolate cookie dough?
package of sugar cookie dough: $5, package of double chocolate cookie dough: $20
39) New York City is a popular field trip destination. This year the senior class at High School A and
the senior class at High School B both planned trips there. The senior class at High School A
rented and filled 5 vans and 12 buses with 445 students. High School B rented and filled 10 vans
and 7 buses with 380 students. Each van and each bus carried the same number of students. Find
the number of students in each van and in each bus.
Van: 17, Bus: 30
40) Kayla and Arjun each improved their yards by planting hostas and ornamental grass. They
bought their supplies from the same store. Kayla spent $44 on 2 hostas and 4 bunches of
ornamental grass. Arjun spent $124 on 10 hostas and 8 bunches of ornamental grass. Find the
cost of one hosta and the cost of one bunch of ornamental grass.
hosta: $6, bunch of ornamental grass: $8
41) Coach Slover has a combination of 25 nickels and dimes in his pocket. If he has $0.95, how many nickels and dimes does he have?
System of Equations _____________________ Nickels _____________
_____________________ Dimes _____________
42) Coach Laurens needs $2.45 to pay for a Monster Energy drink. He uses a combination of 14 quarters and dimes
to pay the cashier. How many of each coin does he use?
System of Equations _____________________ Nickels _____________
_____________________ Dimes _____________
43) Dr. Whaley finds 19 different nickels and dimes underneath the cushions of his couch. When he totaled up his findings, he had $1.25. How many Nickels and Dimes did he have? System of Equations _____________________ Nickels _____________
_____________________ Dimes _____________
X= NICKELS y=Dim±sfChAN$9,Eg§0
•
sx+y=25\×t±E±I×=
×= 11
xios0.05×+0.104=1.95* "y= 11=14
-0.05×-0.054=-1.25.fr#gY=l4X=Q4ARTER5Xty=l4
Ytmnes Quarters
×=7¥.IE#ooiYsNs4?''±¥¥E4=7+-0.154=-1.05
¥ a4=7
-
Xty=l9\×±g=.gx= xe 13
nut 0.05×+0.1011=1.25 - y= y=6BY
-0$- 0.05×-0.054=-0.95 31=13
0=0.30075 as
4=6