Free Printable Review of Systems of Equations

1.

True or False:

All systems of linear equations will have at least one solution.

a)

True

b)

False

2.

A system of linear equations has infinitely many solutions if the lines have

a)

The same slope and the same y-intercept

b)

The same slope and different y-intercepts

c)

Different slopes and different y-intercepts

d)

Different slopes and the same y-intercept

3.

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

a)

4y = 3x + 64

8y = x + 68

b)

4y = 3x + 64

8y = x + 60

c)

3x + 4y = 64

x + 8y = 68

d)

3x + 4y = 64

x + 8y = 60

4.

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

a)

4y = 3x + 64

8y = x + 68

b)

4y = 3x + 64

8y = x + 60

c)

3x + 4y = 64

x + 8y = 68

d)

3x + 4y = 64

x + 8y = 60

5.

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

a)

4y = 3x + 64

8y = x + 68

b)

4y = 3x + 64

8y = x + 60

c)

3x + 4y = 64

x + 8y = 68

d)

3x + 4y = 64

x + 8y = 60

6.

Solve the system.

a)

(3, -2, 4)

b)

(2, -3, 1)

c)

(-3, 2, -1)

d)

Infinitely many solutions

7.

Solve the system.

a)

(1, 2, -2)

b)

(1, -3, -2)

c)

(-1, 3, 2)

d)

No Solution

8.

Solve the system.

a)

(5, -6, 3)

b)

(2, 3, -1)

c)

(-4, 2, 5)

d)

No Solution

9.

Solve the system.

a)

(2, -2, 3)

b)

(2, 1, 4)

c)

(-2, 2, -3)

d)

No Solution

10.

Two linear equations with the same set of variables

a)

system of equations

b)

function

c)

association

d)

correlation

11.

The solution to a system of linear equations can be any of the following except

a)

No solution

b)

Exactly one solution

c)

At least one solution

d)

Infinitely many solutions

12.

If a system of linear equations has no solution, then the lines in the system are

a)

Skewed

b)

Perpendicular

c)

Parallel

13.

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

a)

(-1,-3)

b)

(1,5)

c)

(1,3)

d)

(2,4)

14.

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

a)

(6,-4)

b)

(-4,6)

c)

(4,6)

d)

(6,4)

15.

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

16.

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

a)

yes

b)

no

17.

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

a)

infinite solutions

b)

no solution

c)

one solution

18.

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

a)

yes

b)

no

19.

This system has _____ solutions

a)

no

b)

1

c)

2

d)

Infinitely many

Review of Systems of Equations

Total questions: 19

Worksheet time: 19mins

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