Free Printable Review of System of Equations and Inequalities

1.

Check to see if (-2,1) is a solution to the following system:
x+2y=0
4x+3y=1

a)

yes

b)

no

2.

An inequality using a > or a < has a ___________ line

a)

invisible

b)

solid

c)

dashed

3.

A system of equations that looks like this has ....

a)

infinite solutions

b)

no solution

c)

one solution

4.

Is (3,-4) a solution to this system?

a)

yes

b)

no

5.

Pick the ordered pair that is NOT a solution

a)

(0,0)

b)

(1,-1)

c)

(2,0)

d)

(4,-4)

6.

Solve the following system of equations:
2x+3y=17
y=4x+1

a)

(-1,-3)

b)

(1,5)

c)

(1,3)

d)

(2,4)

7.

Solve using any method:
2x+3y=10
-2x+y=14

a)

(6,-4)

b)

(-4,6)

c)

(4,6)

d)

(6,4)

8.

When you come across a solution that reads 3=4, your answer would be.....

a)

no solution

b)

all real numbers

c)

3 pizzas = 4 hungry hungry hippos

d)

one solution

9.

When you come across a solution that reads 4=4, your answer is...

a)

no solution

b)

all real numbers

c)

4

10.

The sum of 2 numbers is 33. The smaller number is 8 less than 7 times lager number.
Let x= the smaller number and y=the larger number.
Pick which system of equations follows this problem.

a)

x=8-7y
x+y=33

b)

x=7y-8
x+y=33

c)

7x+8y=33
x+y=n

d)

2+x=33
x=8y-7

11.

You have a total of 17 coins. All of your coins are nickels and dimes. The total value of the coins is $1.35. Which system of equations represents this situation?

a)

n+d=17
.05n+.10d=1.35

b)

.05n+.10d=17
n+d=1.35

c)

.25n+.10d=1.35
n+d=17

12.

For the inequality:
y>3x-5
Would you shade (0,0) or shade the other side?

a)

shade (0,0)--it is a solution

b)

Shade the other side--(0,0) is not a solution

13.

An inequality using a ≤ or ≥ is graphed using a

a)

solid line

b)

dashed line

c)

invisible line

d)

no line!

14.

A point that is on a dashed line is.....

a)

a solution

b)

not a solution

15.

Solve the following system:
A farmer is in his field and knows he has 13 animals. His animals are made up of chickens and cows. The farmer can see that he has 34 legs in all but needs to know how many of each animal he has.

a)

4 cows, 9 chickens

b)

4 cows, 2 chickens

c)

9 cows, 4 chickens

d)

9 cows, 2 chickens

16.

Solve the following equations for x and y:
-6x+6y=6
6x-3y=12

a)

6,5

b)

5,6

c)

4,4

d)

2,4

17.

What is the value of z in the system of equations below?

2x-y+z=10

4x+2y-5z=10

x-3y+5z=8

a)

-6

b)

-48

c)

-26

d)

Not sure

18.

What is the solution to the system of three equations?
$x-y+z=6$
$2x+3y+2z=2$
$3x+5y+4z=4$

a)

$\left(2,\ -2,\ 2\right)$

b)

$\left(4,\ -4,\ 4\right)$

c)

$\left(2,\ 2,\ 2\right)$

d)

No solution

19.

For a party, you are cooking a large amount of stew that has meat, potatoes, and carrots. The meat costs $6 per pound, the potatoes cost $3 per pound, and the carrots cost $1 per pound. You spend $48.50 on 13.5 pounds of food. You buy twice as many carrots as potatoes. Which system of three equations represents how much food you bought?

a)

$x-y+z=13.5$
$6x-y+z=48.5$
$x-y+z=6$

b)

$x+y+z=48.5$
$6x+3y+z=13.5$
$z=2y$

c)

$x+y+z=13.5$
$6x+3y+z=48.5$
$z=2y$

d)

$x+y+z=13.5$
$6x+3y+z=48.5$
$z+y=2$

20.

For a party, you are cooking a large amount of stew that has meat, potatoes, and carrots. The meat costs $6 per pound, the potatoes cost $3 per pound, and the carrots cost $1 per pound. You spend $48.50 on 13.5 pounds of food. You buy twice as many carrots as potatoes. How much of each ingredient did you buy?

a)

2.5 lb meat, 5 lb potatoes, 6 lb carrots

b)

0 lb meat, 2.5 lb potatoes, 5 lb carrots

c)

5 lb meat, 2 lb potatoes, 5 lb carrots

d)

6 lb meat, 2.5 lb potatoes, 5 lb carrots

21.

The sum of three numbers is 16. The largest number is equal to the sum of the other two, and 3 times the smallest number is 1 more than the largest. What are the three numbers?

a)

The numbers are 3, 5, and 8

b)

The numbers are -4, 5, and 6

c)

The numbers are 3, 10, and 6

d)

The numbers are 2, 6, and 8

22.

A doctor needs at least 60 adults for a medical study. He cannot use more than 40 men in the study. Write a system of inequalities to model the situation.

a)

$x+y\le60$
$x\le40$
where x represents the number of men and y represents the number of women; x and y must be whole numbers.

b)

$x+y\ge60$
$x\le40$
where x represents the number of men and y represents the number of women; x and y must be whole numbers.

c)

$x+y\ge40$
$x\le60$
where x represents the number of men and y represents the number of women; x and y must be whole numbers.

d)

$x+y\le40$
$y\ge60$
where x represents the number of men and y represents the number of women; x and y must be whole numbers.

23.

Write a system of inequalities to describe the shaded figure shown.

a)

$y\ge x-3$
$y>-x-3$
$y\le2x+4$
$y<-\frac{4}{3}x+4$

b)

$y\ge x+4$

Review of System of Equations and Inequalities

Total questions: 23

Worksheet time: 2hrs 44mins

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