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WorksheetsDay 4 - Systems
Total questions: 23
Worksheet time: 12mins
Two hikers begin hiking at the same time from different locations on a trail. The system of equations graphed on the grid represents this situation. Which value best represents the number of hours the two hikers have been hiking when they are the same distance from the start of the trail?
2.8 h
1.3 h
2.5 h
4.5 h
The two types of tickets sold at a baseball game are standard tickets and discounted tickets. The price of a discounted ticket was 80% of the price of a standard ticket. - There were 153 standard tickets sold at the baseball game. - There were 47 discounted tickets sold at the baseball game. - The total amount of ticket sales from the standard and discounted tickets was $2,629.34 The line graphed on the grid represents the first equation in a system of linear equations for this situation. If the second equation in the system is y = 0.80x, what is the best estimate of the price of a discounted ticket?
$13.95
$14.55
$13.25
$11.15
The graph shows two lines representing the equation y = 2x + 5 and x + y = 1.
Which ordered pair is in the solution set for the system of inequalities y≥2x+5 and ? x+y≤1
(-5, 0)
(0, 7)
(5, 0)
(0, -7)
Which graph best represents the solution set for this system of inequalities? x + 2y < -2 y - x < 3
F
G
H
J
Which graph best represents the solution set to this system of inequalities? x+y<1
x−y≤2
A
B
C
D
What is the solution set for the system of linear inequalities shown?
y>−43x+4 y<x−5
Graph the solution set of the system of linear inequalities in the coordinate plane.
The region above the line y=−43x+4 and below the line y=x−5
The region below the line y=−43x+4 and above the line y=x−5
The region above both lines
The region below both lines
Hot dogs and bags of popcorn were sold at a concession stand. One family paid $8.00 for 2 hot dogs and 3 bags of popcorn. Another family paid $16.50 for 5 hot dogs and 4 bags of popcorn. Which system of equations can be used to determine the price in dollars of a hot dog, x, and the price in dollars of a bag of popcorn, y?
5x + 4y = 8
2x + 3y = 16.5
2x + 3y = 8
5x + 4y = 16.5
2x + 5y = 8
3x + 4y = 16.5
3x + 2y = 8
4x + 5y = 16.5
Line n is shown on the coordinate grid. The table of ordered pairs represents some points on line p. Which system of equation represents line n and line p?
3x - y = 2
2x + y = 4
3x + y = -2
2x + y = 4
3x - y = 2
x + 2y = 4
3x + y = -2
x + 2y = 4
The tables of ordered pairs represent some points on the graphs of two different lines.
Which system of equations represents the graph of these two lines?
x - 6y = -90
x - 3y = 27
x + 6y = 90
x + 3y = -27
6x - y = -15
3x - y = 9
6x + y = 15
3x + y = -9
An artist bought a set of 10 paintbrushes that contained x small paintbrushes and y large paintbrushes. The number of small paintbrushes in the set was 4 times the number of large paintbrushes in the set. Which system of equations can be used to find the numbers of small paintbrushes and large paintbrushes in the set?
x + y = 10,
x = 4y
x - y = 10
x = 4y
x + y = 10
y = 4x
x - y = 10
y = 4x
The tables of ordered pairs represent some points on the graphs of two lines. Which system of equations is represented by the two lines?
y = 5x – 7
4x – y = 4
y = 5x – 7
4x + y = 12
y = 7x – 9
4x – y = 4
y = 7x – 9
4x + y = 12
A system of equations is graphed on the grid. Which system of equations is best represented by the graph?
y = (2/5)x - 8
y = -(3/5)x - 3
y = (2/5)x - 3
y = -(3/5)x - 8
y = (5/2)x - 8
y = -(5/3)x - 3
y = (5/2)x - 3
y = -(5/3)x - 8
A system of linear equations is represented by line h and line j. A table representing some points on line h and the graph of line j are shown. Which system of equations is best represented by line h and j?
y=54x+1
y=34x−5
y=43x−5
y=45x+1
y=−34x−5 y=−54x+1
y=−43x−5
y=−45x+1
Two customers purchased coffee and doughnuts at a coffee shop. Each cup of coffee costs the same amount, and each doughnut costs the same amount. - The first customer paid $4.90 for 1 cup of coffee and 2 doughnuts. - The second customer paid $8.60 for 2 cups of coffee and 3 doughnuts. What is the cost of 1 cup of coffee?
$2.50
$1.20
$4.90
$3.70
A system of linear equations is shown. 6x – 2y = 10 y = 3x – 5 Which statement about the system is true?
The system has one solution, (–1, –8).
The system has one solution, (3, 4).
The system has no solutions.
The system has infinitely many solutions.
What is the solution to this system of equations? –3x + 5y = 21 6x – y = –15
(2, 27)
(–2, 3)
(2, 0)
(–3, –3)
A company advertises on two websites. Each website charges a different amount based on the number of clicks on the advertisement. The table shows the number of clicks on each website and the total cost for each of two days.
What is the cost per click on Website 1?
$1.85
$5.38
$2.20
$2.70
A system of linear equations is shown. x - 3y = 7 x - 2y = 2 What is the value of x in the solution to this system of equations?
5
-5
8
-8
Dance lessons are offered at two studios. The cost of dance lessons at each studio is shown. - Studio Q charges a $30 registration fee plus $80 per month. - Studio R charges a $105 registration fee plus $65 per month. After how many months will the total cost of the dance lessons be equal at the two studios?
5
280
9
430
What is the solution to this system of equations? 2x + y = 40 x – 2y = –20
(12, 16)
(15, 17.5)
There is no solution.
There are an infinite number of solutions.
A mail carrier delivers mail on one of two different routes: a morning route or an afternoon route. Each workday the mail carrier is assigned one of these two routes. • Last month the mail carrier delivered mail on the morning route 16 times and on the afternoon route 12 times, for a total distance traveled of 141 miles. • This month the mail carrier delivered mail on the morning route 10 times and on the afternoon route 15 times, for a total distance traveled of 123.75 miles. What is the distance of the morning route in miles?
5.25 mi
6.00 mi
4.75 mi
5.00 mi
The function f(x) = –4x + 8 represents the first of two equations in a system of linear equations. The second equation in the system has a different slope than the first equation. Which statement is true about the solution to the system of equations?
The system has no solutions.
The system has exactly one solution.
The system has exactly two solutions.
The system has infinitely many solutions.
Which graph best represents this system of equations and its solution? 2x = 6 - y
5x - 4y = 28
A
B
C
D
