Free Printable Unit 4 System Test Review

1.

What is the solution to the system of linear equations? (a)

Choose from the below words

(8,4)

(4,8)

(4,0)

(0,-4)

2.

What is the number of solutions for this system of equations? (a)

Choose from the below words

None

1

2

3

3.

How many solutions does the following system of equations have?

$4x-3y=2$

$8x-6y=4$

a)

2

b)

1

c)

No solutions

d)

Infinite many solutions

4.

What is the y-value of the solution for the system of equation shown? (Type your answer, no spaces)

$2x=4y-6$

$4x+2y=-2$

y=

(a)

5.

Look at the system of equations.

$x-5y=11$

$-3x+y=-5$

What is the solution to this system of equations?

(Drag and drop the correct values into the ordered pair below)

( (a) , (b) )

Choose from the below words

1

-2

3

-1

5

6.

What is the solution to the system of equations?

a)

(0,0)

b)

(0,3)

c)

(3,1)

d)

(4.5,0)

7.

🐠 Aquarium Trip

A large group of 70 people, consisting of adults and students, are going to the aquarium. An adult ticket cost $5.00 and a student ticket cost $2.00. The group total ticket cost is $305.00.

Let x represents the number of adults and y the number of students.

Write a system of linear equations to represent this situation. How many adults went to the aquarium?

a)

55 adults

b)

15 adults

c)

70 adults

d)

40 adults

8.

🍪 Hector & Ivan’s Baking Goals

Hector gets paid $4 for baking cookies and $15 for baking cakes. Hector want to make at least $281. Ivan makes $5 for baking cookies and $12 for baking cakes. Ivan wants to make at least $250.

Let x represents the number of baked cookies and y the number of baked cakes.

Write a system of inequalities to represent this situation. Which of the following combinations of cookies and cakes could help both Hector and Ivan reach their goals?

a)

8 cookies and 17 cakes

b)

10 cookies and 10 cakes

c)

17 cookies and 14 cakes

d)

14 cookies and 16 cakes

9.

Which inequality best represents the line shown on the grid?

a)

$y>\frac{1}{2}x+3$

b)

$y\le2x-3$

c)

$y\ge2x-3$

d)

$y\le\frac{1}{2}x+3$

10.

Which inequality best represents the line shown on the grid?

a)

$y\ge x+1$

b)

$y<-x+1$

c)

$y<-x+2$

d)

$y<x-1$

11.

Consider the system of inequalities:

$3x+2y\le12$

$2x+4y>8$

Which ordered pair satisfy both inequalities?

a)

x=-4 and y=2

b)

x=6 and y=-2

c)

x=-2 and y=4

d)

x=2 and y=4

12.

Which graph shows the solution set for the system of inequalities?

$y>2x-2$

$y<2x+3$

a)

b)

c)

d)

13.

🎉 Sophia’s Party Budget

Sophia is planning to host a party and needs to buy two types of supplies: balloons and streamers. The party store sells balloons for $2 each and streamers for $3 each. Sophia has a budget of $30.

Let x represent the number of balloons and y represent the number of streamers Sophia buys.

Which inequality represents the situation?

a)

$2x+3y\le30$

b)

$2x+3y\ge30$

c)

$2x+3y=30$

d)

$x+y\le30$

14.

Look at the graph for this inequality in 2 variables. Which points are NOT included in the solution set of the system of inequalities?

(Select all that apply.)

a)

(-2,-2)

b)

(2,-1)

c)

(0,0)

d)

(-1,2)

e)

(1,1)

15.

Given the graph of the following system of linear inequalities:

$3y\ge4x+2$

$y+3x\ge2$

Which region on the graph represents the solution set for this system of inequalities?

a)

1

b)

2

c)

3

d)

4

16.

☕ Starbucks Stop

Hector to Starbucks and got coffee and pastries. On Friday, he paid $25 for 1 coffee and 3 pastries. On Saturday he paid $20 for 2 coffees and 2 pastries.

Let c represents the price of coffee and p represents the price of pastries.

Which is a system of equations that could be used to determine the amount of each item?

a)

2c+2p=25

c+3p=20

b)

c+3p=25

2c+2p=20

c)

3c=25

5p=20

d)

c+2p=20

2c+3p=25

17.

🍽️ Maria’s Fundraising Budget

Maria is organizing a fundraising event and needs to buy two types of supplies: tablecloths and plates. The event requires at least 10 tablecloths and no more than 30 plates. Each tablecloth costs $5, and each plate costs $2. Maria has a budget of no more than $100 for these supplies.

Let x represent the number of tablecloths and y represent the number of plates Maria buys.

Which system of inequalities could be used to determine how many tablecloths and plates Maria can buy?

a)

$x\le15$ , $y\le30$ ,

$5x+2y\le150$

b)

$x\le10$ , $y\ge30$ ,

$5x+2y\ge100$

c)

$x\ge10$ , $y\le30$ ,

$5x+2y\le100$

d)

$x\ge5$ , $y\le20$ ,

$5x+2y\le50$

18.

🪴 Héctor’s Garden Budget

Hector is designing a vegetable garden and has allowed himself a $50 for expenses. He finds tomato seeds for $1 and green pepper seeds for $1.50 each.

Let x represents the number of tomato seeds and y the number of pepper seeds.

Write an inequality to represent this situation. Which of the following combinations of tomatoes and pepper seeds could Hector buy considering his budget?

a)

10 tomato and 20 pepper seeds

b)

20 tomato and 25 pepper seeds

c)

10 tomato and 30 pepper seeds

d)

30 tomato and 15 pepper seeds

19.

Which inequality does (3,-6) satisfy?

a)

$y>-2x+2$

b)

$y<-2x-2$

c)

$y>2x+1$

d)

$y<2x+1$

20.

Which system of inequalities has no solution? Hint: It has no double shaded area.

a)

$y\le3x+2$

$-3x+y\ge3$

b)

$-\frac{1}{3}x+y<2$

$y-3\ge-3x$

c)

$y\ge-3x+2$

$y+3x<3$

d)

$y+2\ge-3x$

$y<-\frac{1}{3}x+3$

Unit 4 System Test Review

Total questions: 20

Worksheet time: 31mins

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