Quiz about Writing System of Equations

Question 1

There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?

Accepted Answer

x + y = 15
4x + 2y = 44

Answer

4x + 2y = 15
x + y = 44

Answer

x = 2y + 44
4x = y + 15

Answer

2x - 4y = 44
x - y = 15

Question 2

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

Accepted Answer

x + y = 33
x = 2y - 3

Answer

x + y = 33
y = 2x - 3

Answer

x + y = 33
x = 3 - 2y

Answer

x + y = 3
x = 33 - 2y

Question 3

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

Accepted Answer

4x + 6y = 13

3x + 7y = 13.5

Answer

4x + 6y = 3

13.5x - 13y = 6

Answer

x + y = 4

x - y = 6

Answer

4x - 6y = 13

3x - 7y = 13.5

Question 4

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

Accepted Answer

S + A = 530
3S + 4A = 1740

Answer

S + A = 530
4S + 3A = 1740

Answer

S + A = 1740
3S + 4A = 530

Answer

S + A = 1740
4S + 3A = 530

Question 5

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

Accepted Answer

t + n = 54

t = 3n + 8

Answer

t + n = 54

n = 3t + 8

Answer

t + n = 54

t = 3n - 8

Answer

t + n = 8

t = 3n + 54

Question 6

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

Accepted Answer

x + y = 49

20x + 50y = 1430

Answer

x + y = 1430

20x + 50y = 49

Answer

x + y = 49

10x + 5y = 1430

Answer

x + y = 49

x + y = 1430

Question 7

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

Accepted Answer

5q + 2z = 1.32
3q + 1z = 0.75

Answer

5q + 2z = 1.32
1z = 0.75

Answer

q + z = 1.32
q + z = 0.75

Answer

5q + 2z = 0.75
3q + 1z = 1.32

Question 8

Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

Accepted Answer

4x+3y=134
3x+3y=120

Answer

x+y=134
x+y=120

Answer

3x+3y=134
4x+3y=120

Answer

7xy=134
6xy=120

Question 9

A ________________ is a set of two or more equations that have the same variables.

Accepted Answer

system of equations

Answer

solution of a system

Answer

elimination method

Answer

table

Question 10

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

Accepted Answer

3H + 2D = 315

2H + 4D = 450

Answer

3H + 2D = 450

2H + 4D = 315

Answer

2H + 4D = 315

3H + 2D = 450

Answer

3H + 2D = 315

2H + 2D = 135

Question 11

There are 50 donkeys and chickens on a far.  There are a total of 174 legs.  Which system below can be used to figure out how many of each animal the farm has?

Accepted Answer

d + c = 50
4d + 2c = 174

Answer

d + c = 174
4d + 2c = 50

Answer

d + c = 50
2d + 4c = 174

Answer

d + c = 174
2d + 4c = 50

Question 12

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

Accepted Answer

1.5N+0.5S=78.5

N+S=87

Answer

1.5N+0.5S=78.5

1.5N+0.5S=87

Answer

N+S=78.5

1.5N+0.5S=87

Answer

N+S=78.5

N+S=87

Question 13

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child ticket

Accepted Answer

3S+C=38

3S+2C=52

Answer

3S+C=52

3S+2C=38

Answer

3C+S=38

3C+2S=52

Answer

3C+S=52

3C+2S=38

Question 14

Last season two running backs on the Steelers football team rushed a combined (both running backs) total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

Accepted Answer

x + y = 1550

y = 4x

Answer

x + y = 1550

y = x + 4

Answer

y - x = 1550

y = 4x

Question 15

On Monday Joe bought 10 cups of Coffee and 5 Doughnuts for his office at the (total) cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of Coffee and 10 Doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

Accepted Answer

10c + 5d = 16.50

5c + 10d = 14.25

Answer

10c + 5d = 14.25

5c + 10d = 16.50

Answer

c + d = 10

5c + 10d = 16.50

Question 16

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

Accepted Answer

t: Cost of each taco

m: Cost of each glass of milk

Answer

t: # of tacos

m: # of glasses of milk

Answer

t: total cost

m: # of food items

Question 17

Some students want to order shirts with their school logo. One company charges a total of $9.65 per shirt plus a setup fee of $43. Another company charges a total of $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

Accepted Answer

y = 9.65x + 43

y = 8.40x + 58

Answer

y = 9.65 + x

y = 8.40 + x

Answer

y =9.65x

y = 8.40x

Question 18

If a system of equations has no solution, what does the graph look like?

Accepted Answer

parallel lines

Answer

intersecting lines

Answer

skew lines

Answer

intersecting lines

Question 19

This system has _____ solutions

Accepted Answer

0

Answer

1

Answer

2

Answer

Infinitely many

Question 20

What type of system is being illustrated by the graph?

Accepted Answer

one solution

Answer

two solutions

Answer

no solutions

Answer

infinitely many solutions

Question 21

When you graph the exact same equation twice,

Accepted Answer

you will have infinite solutions.

Answer

you will have no solution.

Answer

you will have one solution.

Answer

you will graph a giraffe.

Question 22

What is the solution to this system?

Accepted Answer

(1, -1)

Answer

(-1, 1)

Answer

(0, -2)

Answer

(2, 0)

Question 23

When you graph the exact same equation twice,

Accepted Answer

you will have infinite solutions.

Answer

you will have no solution.

Answer

you will have one solution.

Answer

you will graph a giraffe.

Question 24

How many solutions will this system have?

Accepted Answer

No solution

Answer

One Solution

Answer

I Don't Know

Answer

Infinitely Many Solutions

Question 25

If a system of linear equations has one solution, what does this mean about the two lines?

Accepted Answer

Intersecting lines

Answer

Parallel lines

Answer

the same line

Question 26

If a system of linear equations has infinitely many solutions, what does this mean about the two lines?

Accepted Answer

Same line

Answer

Intersecting lines

Answer

Parallel lines

Question 27

Lesly graphed two lines in order to find the solution to a given system of equations.
What is the solution?

Accepted Answer

(-3,-8)

Answer

(-8,-3)

Answer

(3,-8)

Answer

(8,3)

Question 28

What is the solution to the system?

Accepted Answer

(6, -2)

Answer

(3, -1)

Answer

(2, -6)

Answer

No Solution

Question 29

What is the solution to the system?

Accepted Answer

(1, 3)

Answer

(0, 3)

Answer

(1, -1)

Answer

(-3, 1)

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