Free Printable A.5 Systems of Equations

1.

What is the solution for x given the graph to the systems of equations

(a)

2.

What is the solution to the systems of equations shown in the graph?

a)

1 Solution x=-1/2

b)

1 Solution y=-1/2

c)

Many Solutions

d)

No Solution

3.

What is the solution for y based on the system:

(a)

4.

Find the answer using substitution: Please list your answer as a coordinate (x,y)

(a)

5.

Find the answer to the systems using substitution: List the solution as a coordinate (x,y):

(a)

6.

Solve the given systems of equations using elimination: Write you answer as a coordinate (x,y).

(a)

7.

Find the answer to the systems using elimination: List the answer as a coordinate (x,y):

(a)

8.

Solve the systems with any method you choose: Check all that apply:

a)

x= -5/2

b)

y=-5/2

c)

No Solutions

d)

Infinitely Many Solutions

e)

x=0

9.

Solve the systems with any method you choose: Check all that apply:

a)

x= -5/2

b)

y=-5/2

c)

No Solutions

d)

Infinitely Many Solutions

e)

x=0

10.

What would the solution be to this system of linear equations?

a)

(0,-1.5)

b)

(1, -3)

c)

(5,0)

d)

(0,0)

11.

What would the solution be to this system of linear equations?

a)

(0,0)

b)

(2,2)

c)

(6,0)

d)

(0,4)

12.

When would we get "infinitely many solutions" to a system of equations?

a)

The lines are parallel, never intersecting

b)

The lines cross at one point

c)

The lines are the same and overlap at all points

d)

The lines cross at 2 points

13.

When will we get "no solutions" from a system of equations?

a)

The two lines cross once

b)

The two lines are the same and overlap

c)

The two lines are parallel and never touch

d)

The two lines cross at 2 points

14.

Match the following graphs to the systems of equations

a)

1.

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

$y=\frac{2}{3}x-2$

b)

2.

$y=-x+7$ $y=2x+1$

c)

3.

$y=-2x+4$ $y=-2x+4$

15.

Which of the following graphs would fit the system of equations?

$y=2x-4$

$y=-\frac{1}{2}x+1$

a)

b)

c)

16.

In a pasture, there are horses and chickens. If there are a total of 28 animals and 80 legs, how many chickens and horses are there?

a)

10 horses, 18 chickens

b)

16 horses, 12 chickens

c)

12 horses, 16 chickens

d)

18 horses, 10 chickens

17.

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?

a)

20 Multiple Choice

b)

10 Multiple Choice

c)

15 Multiple Choice

d)

5 multiple choice

18.

The sum of Mr. Micklow and Ms. Craft's age is 55. The difference is 3.
Solve:
x + y = 55
x - y = 3

a)

(26, 23)

b)

(26, 29)

c)

(29, 26)

d)

(29, 32)

19.

What is the solution to this system?
x = 7 - 2y
2x + y = 5

a)

(-1,4)

b)

(4,-1)

c)

(1,3)

d)

(3,1)

20.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

21.

x-y=11
2x+y=19

a)

(10,-1)

b)

(-1,10)

c)

(3,-4)

d)

(6,7)

22.

-4x-2y=-12
4x+8y=-24

a)

(5,6)

b)

(6,-6)

c)

(6,-2)

d)

(4,-3)

23.

7x+4y =12
x + 2y = -4

a)

(-4,4)

b)

(4,4)

c)

(4,-4)

d)

(-4,-4)

24.

x + 2y = -4
x - 2y = 8

a)

(2,5)

b)

(2,-3)

c)

(2,-2)

d)

(-3,2)

25.

7x - 2y = 6
x - 2y = -6

a)

(2,4)

b)

(3,-2)

c)

(1,2)

d)

(-2,-4)

26.

x-4y = 16
5x + 4y = 8

a)

(4,-3)

b)

(-3,4)

c)

(4,3)

d)

(3,-4)

27.

5x - 2y = 6
x - 2y = -2

a)

(2,2)

b)

(2,1)

c)

(1,2)

d)

(-2,-2)

28.

x + y = 3
3x - y = 1

a)

(2,1)

b)

(-1,2)

c)

(1,2)

d)

(-2,-1)

29.

x -2y = -2
3x - 2y = 6

a)

(4,3)

b)

(-3,4)

c)

(-2,-3)

d)

(-3,-4)

30.

3x - 2y = -8
5x + 2y = -8

a)

(1,-4)

b)

(-1,-4)

c)

(-4,1)

d)

(-2,1)

31.

x - 4y = -4
x + 2y = 8

a)

(2,2)

b)

(4,2)

c)

(2,-2)

d)

(4,-2)

32.

x - 2y = 4
3x +2y = 4

a)

(-2,-1)

b)

(4,-1)

c)

(2,-1)

d)

(4,1)

33.

x - 2y = 4
2x -y = -1

a)

(-2,-3)

b)

(-3,-2)

c)

(2,3)

d)

(3,2)

34.

5x + 3y = 6
x - 3y = 12

a)

(3,3)

b)

(-3,-3)

c)

(3,-3)

d)

(3,-2)

35.

x - y = -2
y = -2

a)

(1,-2)

b)

(-1,-2)

c)

(-4,-2)

d)

(4,-2)

36.

2x - 3y = 6
7x - 3y = -9

a)

(3,4)

b)

(4,-3)

c)

(-4,-3)

d)

(-3,-4)

37.

3x + y = 4
x + 2y = -2

a)

(2,2)

b)

(-2,-2)

c)

(2,-2)

d)

(-2,2)

38.

2x + y = -3
x - 2y = -4

a)

(-2,1)

b)

(1,-2)

c)

(2,1)

d)

(1,2)

39.

x = - 3
2x + 3y = 6

a)

(4,3)

b)

(-4,3)

c)

(-3,4)

d)

(3,-4)

40.

x + 4y = -8
5x - 4y = -16

a)

(4,1)

b)

(1,4)

c)

(-4,-1)

d)

(-1,-4)

41.

2x - 3y = 6
7x - 3y = -9

a)

(-3,-4)

b)

(3,4)

c)

(-4,-3)

d)

(4,3)

42.

5x - 4y = =-16
x+ 2y = -6

a)

(-4,-1)

b)

(5,-1)

c)

(-5,-1)

d)

(4,1)

43.

Find the solution to the system.
y = x-6
y = -3x + 2

a)

(0, -6)

b)

(6, 0)

c)

(-4, 2)

d)

(2, -4)

44.

A ________________ is a set of two or more equations that have the same variables.

a)

solution of a system

b)

elimination method

c)

system of equations

d)

table

45.

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

a)

t: # of tacos

m: # of glasses of milk

b)

t: Cost of each taco

m: Cost of each glass of milk

c)

t: total cost

m: # of food items

d)

t: Cost of each glass of milk

m: Cost of each taco

46.

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

a)

1s + 3c = 38

2s + 3c = 52

b)

3s + 1c = 38

3s + 2c = 52

c)

s + c = 38

s + c = 52

d)

3s + 3c = 38

1s + 2c = 52

47.

Beth and Nora each improved their yards by planting rose bushes and ornamental grass. They bought their supplies from the same store. Beth spent $36 on 6 rose bushes and 2 bunches of ornamental grass. Nora spent $66 on 4 rose bushes and 6 bunches of ornamental grass. Which equations could you use to solve this system?

a)

$36+6x=2y$
$66+4x=6y$

b)

$6x+2y=36$
$4x+6y=66$

c)

$6x-2y=36$
$4x-6y=66$

d)

$y=8x+36$
$y=10x+66$

48.

Beth and Nora each improved their yards by planting rose bushes and ornamental grass. They bought their supplies from the same store. Beth spent $36 on 6 rose bushes and 2 bunches of ornamental grass. Nora spent $66 on 4 rose bushes and 6 bunches of ornamental grass. What is the cost of one rose bush and the cost of one bunch of ornamental grass?

a)

rose bush: $1, bunch of ornamental grass: $10

b)

rose bush: $4, bunch of ornamental grass: $7

c)

rose bush: $3, bunch of ornamental grass: $9

d)

rose bush: $2, bunch of ornamental grass: $5

49.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

a)

3x + 2y = 315

2x + 4y = 450

b)

3x + 2y = 450

2x + 4y = 315

c)

2x + 2y = 315

3x + 4y = 450

50.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. How long does it take her to do a haircut?

3x + 2y = 315

2x + 4y = 450

a)

45 minutes

b)

90 minutes

c)

60 minutes

d)

30 minutes

A.5 Systems of Equations

Total questions: 50

Worksheet time: 3hrs 42mins

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