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Solving Systems of Linear Equations

Total questions: 60

Worksheet time: 4hrs 10mins

Name
Class
Date
1.

A system of linear equations is shown. What is the solution to the system?

a)

1

b)

-2

c)

(1, 2)

d)

(1, -1)

2.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
3.
The solution to a system of equations is any ordered pair that makes both equations true. 
a)
TRUE
b)
FALSE
4.
Steffen graphed two lines in order to find the solution to a given system of equations.
What is the solution?
a)
(-3,-8)
b)
(-8,-3)
c)
(3,-8)
d)
(8,3)
5.
What is the solution to this system?
a)
(-2, -2)
b)
(2, -2)
c)
(-2,2)
d)
(2, 2)
6.
This system has _____ solutions
a)
0
b)
1
c)
2
d)
Infinitely many
7.

When you graph two linear equations and they form the same line,

a)

you will have no solution.

b)

you will have one solution.

c)

you will have infinite solutions.

d)

you will graph a giraffe.

8.
Lisa and Tammy are selling items at the craft show.  Which might be a reasonable solution from the graph showing the number of items sold when they both have earned the same amount?
a)
(1, 12)
b)
(3, 19)
c)
(5, 25)
d)
(0, 10)
9.

Parallel Lines have how many solutions?

a)

One Solution

b)

Infinitely Many Solutions

c)

No Solutions

d)

As many solutions as you want

10.

Intersecting Lines have how many solutions?

a)

One Solution

b)

Infinitely Many Solutions

c)

No Solutions

d)

As many solutions as you want

11.

A system of linear equations with NO SOLUTIONS will have which of the following characteristics?

a)

Same Slope but Different Y-Intercepts

b)

Different Slopes but Y-Intercepts doesn't matter

c)

Same Slope Same Y-Intercept

d)

No Slopes and X-Intercepts

12.

A system of linear equations that has ONE SOLUTION will have which of the following characteristics?

a)

Same Slope but Different Y-Intercepts

b)

Different Slopes

c)

Same Slope Same Y-Intercept

d)

No Slopes and X-Intercepts

13.

Coincident Lines, two linear equations that form the same line, have how many solutions?

a)

One Solution

b)

Infinitely Many Solutions

c)

No Solutions

d)

As many solutions as you want

14.

A system of equations with infinite solutions have which of the following characteristics?

a)

Same Slope but Different Y-Intercepts

b)

Different Slopes but Y-Intercepts doesn't matter

c)

Same Slope and Same Y-Intercept

d)

No Slopes and X-Intercepts

15.

Which of the following systems of linear equations represent parallel lines?

a)

y = 2x - 3

2y = 4x + 6

b)

y = x + 2

y = 2x + 1

c)

y = -3

x = -4

d)

y = 2x + 4

y = 2x + 4

16.

Which image shows a system of linear equations with one solution?

a)
b)
c)
d)
17.

Which image shows a system of linear equations with no solutions?

a)
b)
c)
d)
18.

Which image shows a system of linear equations with infinitely many solutions?

a)
b)
c)
d)
19.
Solve the following system by graphing.  What is the solution?
a)
Infinite number of solutions
b)
(3, 3)
c)
(3, -3)
d)
(-3, 3)
20.
How many solutions does this system of equations have?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
d)
Two Solutions
21.
How many solutions will this system have? 
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
22.
If a system of equations has infinitely many solutions, what does the graph look like? 
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
the same line (coinciding lines)
23.
If a system of equations has no solution, what does the graph look like? 
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
the same line (coinciding lines)
24.

Is (1,10) a solution to

y=7x+5

y=x+9

a)

yes

b)

no

25.

Is (1,7) a solution for

y=3x+4

y=x+6

a)

yes

b)

no

26.
This system has _____ solutions
a)
0
b)
1
c)
2
d)
Infinitely many
27.

Without graphing, decide if the system, y = x - 4 and y = x - 3 has one solution, infinitely many solutions, or no solution.

a)

one solution, equations have the different slopes

b)

two solution, the lines intersect at two points

c)

no solution, the slopes are the same and the y-intercepts are different

d)

infinitely many solutions, the slope and the y-intercept are the same

28.

The first equation in the system is y = 2x - 3. Pick a second equation from the list below so that the system has ONE SOLUTION.

a)

y = 2x + 4

b)

y = 1/2x + 2

c)

-2x + y = -3

d)

2y = 4x - 6

29.

The first equation in the system is y = 2x - 3. Pick a second equation from the list below so that the system has NO SOLUTIONS.

a)

y = 2x + 4

b)

y = 1/2x + 2

c)

-2x + y = -3

d)

2y = 4x - 6

30.

The first equation in the system is y = 2x - 3. Pick a second equation from the list below so that the system has INFINITELY MANY SOLUTIONS.

a)

y = 2x + 4

b)

y = 1/2x + 2

c)

2x + y = -3

d)

2y = 4x - 6

31.
Solve the following system by graphing.  What is the solution?
a)
(-4, 2)
b)
(4, 2)
c)
(2, -4)
d)
(2, 4)
32.
Solve the system by graphing:
y = 6x - 4
y = -x + 3
a)
(1, 2)
b)
(2, 1)
c)
(4, 5)
d)
(2, 4)
33.
Solve the system of equations by substitution.
y = -4x + 5
y =  3x - 16
a)
(-3, -25)
b)
(3,-7)
c)
(11, 17)
d)
(21, 47)
34.
Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount? 
a)
y = 9.65 + x
y = 8.40 + x
b)
y = 9.65x + 43
y = 8.40x + 58
c)
y =9.65x
y = 8.40x
d)
y = 9.65x - 43
y = 8.40x - 58
35.
A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount? 
a)
y = 6.80 + .65x
y=7.30+.90x
b)
x + y = 6.80
x + y = 7.30
c)
y = 6.80+.90x
y = 7.30 + .65x
d)
y + .90x = 6.80
y + .65x = 7.30
36.
What is the solution to this system of linear equations? 
Use substitution.

y = -2x - 6
-2x + y = 6
a)
(0, -3)
b)
(-3, -12)
c)
(-3, 0)
d)
(3, -12)
37.
A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. How many toppings can you get at each Pizzeria so that the price of a large pizza is the same? 
a)
3 toppings
b)
1 topping
c)
2 toppings
d)
4 toppings
38.

Match the system of linear equations to the corresponding graph.

 y=2x−5y=2x-5  
 y=−32x+2y=-\frac{3}{2}x+2  

a)
b)
c)
d)
39.

Solve the system of linear equations by substitution.


 y=3x−1y=3x-1  
 y=x−7y=x-7  

a)

(2, 5)

b)

(-1, 7)

c)

(-3, -10)

d)

(4, 4)

40.

Solve the system of linear equations by substitution.


 y = −2x+5y\ =\ -2x+5  
 3x+5y=183x+5y=18  

a)

(1, 3)

b)

(6, 3)

c)

(-5, 0)

d)

(2, 7)

41.

Match a sentence with this equation: C = 7.50p + 3.00C\ =\ 7.50p\ +\ 3.00  

a)

JB's Deli charges $ 0.75 for each pizza and $3.00 per topping

b)

Sally's Pizza  charges $3.00 per pizza with a $7.50 delivery fee

c)

Pizza Time charges $7.50 for each pizza and $.30 for the delivery fee

d)

Pizza Planet charges $7.50 per pizza with a $3.00 delivery fee

42.
Mr. Z is starting his own car club, there is a $30 join up fee and a $5 monthly fee. 
a)
y = 30x + 5
b)
y = 5x + 30
43.

A canoe rental service charges a $20 transportation fee and $30 dollars an hour to rent a canoe. Write an equation representing the cost, y, of renting a canoe for x hours.

a)

y = 30x + 20

b)

y = 20x + 30

c)

y = 50x

d)

y = 60x

44.
The equations of two lines are:
 2x-y=4 and y=-2x+8.
What is the value of x in the solution for this system?
a)
x=8
b)
x=3
c)
x=11
d)
x=5
45.

Is the function represented by the table linear or nonlinear?

a)

Linear

b)

Nonlinear

46.
Is this function linear or nonlinear?
a)
Linear
b)
Nonlinear
47.
Is the graph pictured a linear or nonlinear function?
a)
Linear
b)
Nonlinear
48.
Is the table linear or nonlinear?
a)
Linear
b)
Nonlinear
49.

Is this function linear or nonlinear?

a)

Linear function

b)

Nonlinear function

50.

Which graph is linear?

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

51.
Which equation(s) represent nonlinear functions?
a)
Equation 1, only
b)
Equations 1 and 3, only
c)
Equations 1, 2, and 3, only
d)
Equations 1, 2, 3, and 4
52.
Which equations represent linear functions?
a)
Equations 1 and 2, only
b)
Equations 1 and 4, only
c)
Equations 2 and 3, only
d)
Equations 1, 3, and 4, only
53.

Is the following equation linear or nonlinear?

HINT: use your calculator to graph the equation to look at the graph

a)

Linear

b)

Nonlinear

54.

Is the following equation linear or nonlinear?

HINT: use your calculator to graph the equation to look at the graph

a)

Linear

b)

Nonlinear

55.

Between 4 and 8 seconds the helicopter's speed is .....................

a)

Increasing

b)

Decreasing

c)

Stationary

56.
The sales record for a recent hit CD at Tony’s Music Store is shown on the graph.  Which statement best describes the sales of this CD?
a)
Sales rapidly increased, reached a peak, and then gradually decreased.
b)
Sales gradually increased, reached a peak, and then leveled off.
c)
Sales rapidly increased, reached a peak, and then rapidly decreased
d)
Sales remained constant throughout the time period.
57.
According to the graph how far does the person travel in the first 5 seconds?
a)
2 m
b)
10 m
c)
0 m
d)
5 m
58.

What is the rate of the bicycle from 9am to 11 am?

a)

20 miles/hour

b)

30 miles/hour

c)

60 miles/hour

d)

15 miles/hour

59.
Between which seconds is the line INCREASING?
a)
Between 7 and 12 seconds
b)
Between 0 and 1 seconds
c)
Between 1 and 5 seconds
d)
Between 12 and 13.5 seconds
60.
Between which seconds is the line DECREASING?
a)
Between 7 and 12 seconds
b)
Between 0 and 1 seconds
c)
Between 1 and 5 seconds
d)
Between 12 and 13.5 seconds

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