wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Algebra Review Quiz #4 Systems of Equations/Inequalities

Total questions: 30

Worksheet time: 55mins

Name
Class
Date
1.

What is the solution?

a)

1

b)

-2

c)

(1, 2)

d)

(1, -1)

e)

Many Solutions

2.

This system has _____ solutions

a)

0

b)

1

c)

2

d)

Infinitely many

e)

(-3,-2)

3.

What is the solution?

(Hint: Both lines are graphed over each other)

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

d)

Two Solutions

e)

Not Enough Information

4.

Solve the following system by graphing. What is the solution?

a)

(-2, -4)

b)

(2, -4)

c)

(-2, 4)

d)

(2, 4)

e)

Infinity Many Solutions

5.

Solve the following system by graphing. What is the solution?

a)

Infinite number of solutions

b)

(3, 3)

c)

(3, -3)

d)

(-3, 3)

e)

No solutions

6.
It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?
a)
2x + 3y ≤ 18
b)
x + y ≤ 6
c)
x + y ≤ 9
d)
3x + 2y ≤ 18
7.

Rachel owns a car and a moped. She has at most 12 gallons of gas to be used between the car and the moped. The car's tank holds at most 10 gallons and the moped's 3 gallons. The mileage for the car is 20 mpg and for the moped is 100 mpg. Which of the following points is NOT a vertex of the shaded region?

a)

(10,2)

b)

(6, 6)

c)

(0,0)

d)

(0,3)

e)

No Solution

8.

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans he plants and $3,000 for every acre he plants with corn can be modeled by P=4000x+3000y . What is the maximum profit that she can earn?

a)

$15,000

b)

$21,000

c)

$18,000

d)

$25,000

e)

Their is no solution region therefore there is no maximum profit.

9.

Which of the following represents the situation:

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?

a)

1.5x+0.5y=78.5

x+y=87

b)

1.5x+0.5y=78.5

1.5x+0.5y=87

c)

x+y=78.5

1.5x+0.5y=87

d)

x+y=78.5

x+y=87

e)

This is a systems of inequalities so none of the equations are correct.

10.

Which of the following represents the situation:

Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing.

a)

x+y≤300

7.5x+5.5y≥2000

b)

x+y<300

7.5x+5.5y≥2000

c)

x+y≤300

7.5x+5.5y≤2000

d)

x+y>2000

7.5x+5.5y≤300

e)

This is a systems of equations so none of the inequalities are correct.

11.

Which of the following represents the situation:

Eiko is drawing caricatures at a fair for 8 hours (480 minutes). She can complete a small drawing in 15 minutes and charges $10 for the drawing. She can complete a larger drawing in 45 minutes and charges $25 for the drawing. Eiko hopes to make at least $200 at the fair.

a)

10x+15y≤480

45x+25y≥250

b)

10x+25y≤200

15x+45y≤480

c)

10x+25y>200

15x+45y<480

d)

10x+25y≥200

15x+45y≤480

e)

This is a systems of equations that would be solve most simply by using elimination.

12.

Ron has $1.65 in a collection of only dimes and quarters. Which are possible solutions for the amount of quarters Ron has, check ALL that apply.

a)

1 Quarter

b)

2 Quarters

c)

3 Quarters

d)

5 Quarters

e)

Not enough information

13.

What is the solution to the systems

x+y=5

x-y=3

a)

(8,3)

b)

(5,2)

c)

(6,-1)

d)

(4,1)

e)

No solutions

14.

What is the solution to the systems:

3x+y=11

y=x+3

a)

(4,7)

b)

(0.5,3.5)

c)

(-2,17)

d)

(2,5)

e)

No Solution

15.

What is the solution to the systems:

y=-3x-2

6x+2y=-4

a)

(6,2)

b)

(-1,-5)

c)

(-2,-8)

d)

Infinity Many Solutions

e)

No Solution

16.

Elber bought 11 binders and notebooks from the store and spent $45. Binders cost $6 each and notebooks cost $2.50 each. Which equations would you use to find the numbers of binders, b, and notebooks, n, she purchased

a)

b+n=11

b)

b+n=45

c)

6b+2.5n=11

d)

6b+2.5n=45

e)

2.5b+6n=11

17.

Which ordered pairs are solutions to the inequalities 2x-y>-4 Check all that apply.

a)

(-4,-3)

b)

(1,-6)

c)

(-2,-5)

d)

(8,2)

e)

(-2,0)

18.

Which graph represents the solution to the inequality

x - 4y ≤ -12

a)
b)
c)
d)
e)

The lines on the graph should be dotted so none of the graphs are the correct solution

19.

Which inequality represents the graph?

a)

y≤1/2x-1

b)

y≤3/2x+2

c)

y≥1/2x-1

d)

y>3/2x+2

e)

y<3/2x-1

20.

Which inequality is represented in the graph?

a)

x<-2

b)

x>-2

c)

y<-2

d)

y>-2

e)

Undefined

21.

Which point on the graph in the picture is included in the solution to the following systems of inequalities?

y > 2/3 x+1

5x + 6y < -30

a)

A

b)

B

c)

C

d)

D

e)

None of the points are in the solution region.

22.

Andy says that a systems of two linear equations must have at least one solution as long as the lines have different y intercepts. For example, the equation y=2x+4 and y=4x-6 have different y intercepts and have a solution at (5,14)

Select a pair of linear equations that can be used to disprove Andrea's claim

a)

y=-2/3x+4

y=3/2x-4

b)

y - 2x=4

4y -8x =16

c)

y+4x=1

y+4x=3

d)

y=5/3x+3/5

y=3/5x+5/3

e)

Andy is correct any equations with different y-intercepts have exactly one solution, a coordinate pair.

23.

Which of the following is the graph for the systems of inequalities:

y ≤ -2x + 5

y > 3x - 1

a)
b)
c)
d)
e)

The shaded region should be on the top, so none of the graphs are shaded correctly

24.

If you solve a systems of equations by substitution and your substituted equation is 3y=3y+6, how many solutions does the systems have?

a)

No Solutions

b)

1 Solution

c)

2 Solutions

d)

Infinitely Many Solutions

e)

Not enough information to know

25.

After doing elimination your equation works out to be 0x+0y=0, how many solutions does your systems of equations have?

a)

No Solutions

b)

1 Solution

c)

2 Solutions

d)

Infinitely Many Solutions

e)

Not Enough Information

26.

After doing elimination you get an equation of -5x+0y=-27, how many solutions does your systems of equations have?

a)

No Solutions

b)

1 Solution

c)

2 Solutions

d)

Infinity Many Solutions

e)

Not Enough Information

27.

If a systems of linear inequalities with 2 equations has no solution which of the following must be true? Choose both correct answers!

a)

The Lines are Parallel

b)

The Lines are Perpendicular

c)

Both Lines are Less than y

d)

Both Lines are Greater than y

e)

One Line is Greater than y and One Line is Less than y

28.

There are two types of memberships to the water park in Moses Lake, an unlimited membership cost $70 for the summer, or a summer membership cost $10 plus $5 every visit. How many visit would an individual have to make to make the unlimited membership more cost effective than the summer membership.

a)

The unlimited is always a better deal

b)

10 trips

c)

12 trips

d)

13 trips

e)

The summer membership is always a better deal

29.

Jerry decides he wants to find the solutions of the a systems of equations with a linear are quadratic function. Choose all the solutions of the equation y= -x+2 and y=x2,

a)

(-2,4)

b)

(-1,1)

c)

(0,0)

d)

(1,1)

e)

Infinity Many Solutions

30.

Choose all the coordinate pairs that are a solutions to the systems of inequalities.

a)

(4,0)

b)

(0,4)

c)

The point of intersection of the two lines (1,1)

d)

(0,0)

e)

(8,-8)