Download Unit 4 Test Review Solutions

Algebra 1
Unit 4 Solve Systems of Linear Equations
Unit 4 Test Review
Mathematician: ________________________________
Period:___________
Target 4.1: Solve a system of linear equations graphically/numerically
Directions: Graph the system of linear equations. After solving the system, what is the sum of the x- and y- coordinates of the
solution?
1)
ì5x + y = -1
í
î y = -x + 3
2)
ì y + 4 = -x
í
î-24 + 6 y = 10x
3)
Solution: ______________
Solution: ______________
Sum: ______________
Sum: ______________
4) Describe the types of solutions that a system of linear
equations can have.
ì3y = 9x + 6
í
î-3x - 3y = 24
Solution: ______________
Sum: ______________
5) Describe the graph of a system of linear equations if the
solution is “no solution.”
Directions: Given that one of the lines in the system of linear equations is -3x - y = 5 , choose the equation that
would give the indicated solution.
6) Infinitely many solutions
7) One solution
A) y = -3x -1
A)
y = 4x + 2
B)
y = 2x +10
B)
y = -3x -5
C)
y = -3x -5
C)
y = -3x + 2
Directions: Choose the appropriate graph(s) to answer Questions 8-10. Choose all that apply.
(c) Two solutions
(d) Infinitely many
solutions
(e) Not enough
information
(a) Zero solutions
(b) Exactly one solution
8) A B C D E
Line 1: y-intercept of 7 and decreasing
Line 2: y-intercept of -6 and decreasing
9) A B C D E
Line 3: positive and contains point (-1, 3)
Line 4:
1
y=- x+7
4
10) A B C D E
Line 5: slope of -2 and contains point (2, 4)
Line 6:
y = -2x + 4
Target 4.2: Solve a system of linear equations by substitution
11) Which equation would you use as the substitute in
the following system of linear equations?
12) Which equation would you use as the substitute in
the following system of linear equations?
Equation 1: 3x - 7y = 21
Equation 1: 2x - y = 3
Equation 2 : x = 2x -1
Equation 2 : x + 6 y = 12
Directions: Solve the following systems by substitution.
13)
ì y = -3x - 9
í
î-x - 3y = 11
Solution: ______________
14)
ì-4x + 4 y = 0
í
î x - 3y = 8
Solution: ______________
15)
ì y = 2x + 8
í
îy = x +4
Solution: ______________
Directions: Solve the system of linear equations by substitution. After solving the system, what is the
product of the x- and y- coordinates of the solution?
16)
ì-6x + y = 21
í
î-x + 5y = 18
Solution: ______________
Product: ______________
17)
ì-7x + y = 10
í
î8x = 1- 3y
Solution: ______________
Product: ______________
18)
ì3y + x = 6
í
î2 y + 4x = -16
Solution: ______________
Product: ______________
Target 4.3: Solve a system of linear equations by elimination
Directions: Solve the following systems by elimination.
ì4x - y = 6
19)
í
îx + y = 9
20)
ì8x - 5y = 11
í
îx + y = 3
Solution: ______________
Solution: ______________
Directions: Solve the system. Then select the x-coordinate of the solution.
21)
ì5x = -14 + 2 y
í
î-4x - 5y = -2
A)
0
B)
22)
-2
C) -4
ì3x + 2 y = 3
í
î-x - 5y = -1
A) 1
B) 0
C) -1
Directions: Solve the system. Then find the sum of the x- and y-coordinates of the solution.
23)
ì-3x = -8 + 2 y
í
î-5y = 1+ 4x
Solution: ______________
A) 11
B) -30
ì8 = 20x - 8 y
í
î10x = -8 + 2 y
24)
Solution: ______________
C)
1
A)
-8
B)
12
C) 4
Target 4.4: Write and solve a system of linear equations that models real-world
situations
Directions: Define your variables, write, and solve a system of linear equations that model the given situation.
25) The school that Carlos goes to is selling tickets to the annual talent show. On the first day of ticket sales the
school sold 6 adult tickets and 5 student tickets for a total of $96.40. The school took in $133.60 by selling 12 adult
tickets and 2 student tickets on the second day. What is the price of one adult ticket and one student ticket?
a) Define your variables.
b) Write and solve the linear system.
26) Nicole and Janice each improved their yards by planting hostas and geraniums. They bought their supplies
from the same store. Nicole spent $117.60 on 12 hostas and 12 geraniums. Janice spent $77.80 on 6 hostas and 11
geraniums. If Janice wanted to buy one more hosta and one more geranium, how much would she spend?
a) Define your variables.
b) Write and solve the linear system.
27) Michelle went to the store to buy wrapping paper for the upcoming holiday season. She bought a total of 12
rolls of green and purple wrapping paper for $36.75. If green wrapping paper costs $3.50 and purple wrapping
paper costs $2.75, how many of each role of wrapping paper did she buy?
a) Define your variables.
b) Write and solve the linear system.
Directions: Define your variables, write, and solve a system of linear equations that model the given situation.
28) Ted and Lily are selling cookie dough for a school fundraiser. Customers can buy packages of sugar cookie
dough and packages of chocolate chip cookie dough. Ted sold 5 packages of sugar cookie dough and 7 packages of
chocolate chip cookie dough for $178. Lily sold 3 packages of sugar cookie dough and 7 packages of chocolate chip
cookie dough for $160. If you were to buy 1 of each package of cookie dough, how much would you spend?
a) Define your variables.
b) Write and solve the linear system.
29) Six Flags is a popular field trip destination for many schools. This year the senior class at McHenry High
School and Crystal Lake South High School both planned trips there. MCHS rented and filled 3 vans and 4 busses
with 239 students. CLSHS rented and filled 4 vans and 4 busses with 248 students. Each van and bus carried the
same number of students. How many total students total can one van and one bus hold?
a) Define your variables.
b) Write and solve the linear system.
30) The sum of two numbers is 13 and their difference is 1. Write a system of linear equations to find the two
numbers.
Unit 4 Test Review Solutions
1) Solution: (-1,4) Sum: 3
2) Solution: (-3,-1) Sum: -4
3) Solution: (-2.5,-5.5) Sum: -8
4) A system of linear equations can have three types of solutions: 0 solutions (parallel lines), 1 solution (lines
intersect), or infinitely many solutions (same line)
5) Answers may vary
6) C
7) A
8) A and B
9) B
10)
11) Equation 2
12) Answers may vary
13) (-2,-3)
14) (-4,-4)
15) (-4,0)
16) Solution: (-3,3) Product: -9
17) Solution: (-1,3) Product: -3
18) Solution: (-6,4) Product: -24
19) (3,6)
20) (2,1)
21) B) -2 ==== (-2,2)
22) A) 1 ==== (1,0)
23) Solution: (6,-5) C)1
24) Solution: (-2,-6) A) -8
25) a) A = price of one adult ticket, T = price of one student ticket
ì6A + 5T = 96.40
b) System = í
===== One adult ticket is $9.90 and one student ticket is $7.40
î12A+ 2T = 133.60
26) a) H = price of one hosta, G = price of one geranium
ì12H +12G = 117.60
b) System = í
===== (6 , 3.80) === $9.80
î6H +11G = 77.80
27) a) G = number of rolls of green wrapping paper, P = number of rolls of purple wrapping paper
ì3.5G + 2.75P = 36.75
b) System = í
===== (5,7) ==== 5 rolls of green, 7 rolls of purple
îG + P = 12
28) a) S = price of 1 package of sugar cookie dough, C = price of 1 package of chocolate chip cookie dough
ì5S + 7C = 178
b) System = í
===== (9,19) ==== $28
î3S + 7C = 160
29) a) V = number of students a van can hold, B = number of students a bus can hold
ì3V + 4B = 239
b) System = í
===== (9,53) ==== 1 van and 1 bus can hold 62 students total
î4V + 4B = 248
30) 6 and 7