Free Printable Solving Systems Substitution/Elimination Test

1.

What order is the 5 steps for elimination method?

a)

Place in Standard Form

b)

Determine which variable to eliminate

c)

Add or subtract the equations

d)

Plug variable back into equation

e)

Check your solution

1)

2)

3)

4)

5)

2.

What are the five steps to solving systems using substitution method.

a)

Solve an equation for one variable

b)

Substitute

c)

Solve the equation

d)

Plug back in to find the other variable

e)

Check your solution

1)

2)

3)

4)

5)

3.

In this system

x+3y=9

4x-2y=-6

it'll be easiest to start by solving the first equation for x.

The result of doing so is x=

(a)

4.

In this system

x+3y=9

4x-2y=-6

it'll be easiest to start by solving the first equation for x.

The result of doing so is x=9-3y.

Fill in the blanks to plug that expression in and solve for y:

4(9-3y)-2y =-6

36-12y-2y=-6

36-14y =-6

-14y= (a)

y= (b)

Choose from the below words

-42

3

30

-3

5.

In this system

x+3y=9

4x-2y=-6

we have figured out that x=9-3y, and y=3.

Complete the steps to solve for x:

x=9-3( (a) )

x=9- (b)

x= (c)

The solution to the system is ( (d) , (e) ).

Choose from the below words

3

9

0

y

x

y=3

3y

-9

18

6.

Put the steps for solving by ELIMINATION in order:

a)

Make sure the equations are lined up

b)

Multiply one or both equations by a number to get common but opposite coefficients

c)

Subtract the equations to eliminate one variable

d)

Solve for the remaining variable

e)

Plug that number into either original equation and solve for the other variable

1)

2)

3)

4)

5)

7.

Consider the system

4x+3y=-1

5x+4y=1

Let's say I want to eliminate the y's. What is the least common multiple of 3 and 4?

LCM = (a)

Multiply each equation by a number so that the coefficient of y will be 12, with one positive and one negative.

(b) (4x+3y=-1)

(c) (5x+4y=1)

Choose from the below words

12

4

-3

3

5

1

-1

-12

8.

Consider the system

4x+3y=-1

5x+4y=1

After we do this multiplication, what will the new equations be?

4(4x+3y=-1) ---> (a) x + (b) y= (c)

-3(5x+4y=1) ---> (d) x - (e) y= -3

Choose from the below words

16

12

-4

-15

3

5

1

-1

-12

-3

9.

Consider the system:

4x+3y=-1

5x+4y=1

Which we converted to:

16 x + 12y=-4

-15x - 12y= -3

Combining the equations straight down gives us:

(a) x+ (b) y= (c)

Solving for x, we get x= (d)

Choose from the below words

1

0

-7

3

5

-1

-12

-3

10.

Consider the system:

4x+3y=-1

5x+4y=1

Since we now know that x=-7, solve for y:

4( (a) )+3y=-1

(b) +3y=-1

(c) = (d)

y= (e)

Choose from the below words

-7

-28

3y

27

9

5

7

-12

3

y

11.

Solve for y:

4x-y=3 ---> y= (a) x (b)

Choose from the below words

4

-3

-4

3

3/4

4/3

-1/4

12.

Put the steps for solving by SUBSTITUTION in order:

a)

Solve one equation for x or y

b)

Plug the resulting expression into the other equation

c)

Solve for the first variable

d)

Plug that number into the other equation

e)

Solve for the second variable

1)

2)

3)

4)

5)

13.

what is the variable that will be "eliminated"?

5x - 4y = 11

5x + 4y = -14

a)

x variable

b)

y variables

c)

both variables

14.

What would be the first step in finding the solution using elimination?

2x + 2y = -2

3x - 2y = 12

a)

you cannot solve this using elimination

b)

cross out the 2x and 3x

c)

Add the like terms. The y terms will zero out.

d)

change to slope intercept form and graph

15.

Solve the system by elimination. Show all work.

3x + y = 19

2x - y = 6

a)

(5, 14)

b)

(4, 5)

c)

(5, 4)

d)

(14, 5)

16.

Solve by elimination:

-9x - 4y = -20

5x + 4y = 4

a)

(-4,4)

b)

(4,4)

c)

(4,-4)

d)

(-4,-4)

17.

what does the top equation need to be multiplied by to create a zero pair?

2x - 6y = 20

2x + 5y = -11

a)

-1

b)

1

c)

-2

d)

2

18.

what do you need to multiply the top equation by to make a zero pair:

5x - 2y = 11

-10x + 3y = -4

a)

5

b)

-1

c)

2

d)

-2

19.

Solve by elimination
4x-6y= -6
-2x-12y= -12

a)

(0,1)

b)

(1,0)

c)

(1,1)

d)

(2,1)

20.

Solve by elimination:
3x + 7y = 23
-3x - 7y = -17

a)

No solution

b)

Infinite number of solutions

c)

(-3,3)

d)

(3,3)

21.

5x + y = 9
10x − 7y = −18

a)

(4, -11)

b)

(1, 4)

c)

(-1, 14)

d)

(-4, 29)

22.

Solve the system by elimination.

−6x + 6y = 0
9x − 8y = 4

a)

(4, −9)

b)

Infinite number of solutions

c)

(−9, 4)

d)

(4, 4)

23.

8x + 14y = 4
-6x - 7y = -10

a)

(4, -2)

b)

(-2, 4)

c)

(0, 3)

d)

(4, -2)

24.

-x - 7y = 14
-4x - 14y = 28

a)

(-2, 0)

b)

(0, -2)

c)

(-2, -2)

d)

(0, 2)

25.

If two lines are parallel how many solutions do they have?

a)

1

b)

2

c)

infinite

d)

none

26.

Will the solution (-3, -7) make the following system of equations a true statement?
y = 4x + 5
y = x – 4

a)

YES

b)

NO

27.

Solve by elimination
4x-6y= -6
-2x-12y= -12

a)

(0,1)

b)

(1,0)

c)

(1,1)

d)

(2,1)

28.

Solve the system by elimination.

4x + 12y = −1
−3x − 9y = 0

a)

(10, 1)

b)

(−10, −1)

c)

(10, −1)

d)

No solution

29.

What is the solution to the system?

a)

(0, 3)

b)

(1, -1)

c)

(-3, 1)

d)

(1, 3)

30.

Solve by elimination
-12x-4y= -8
-6x-2y= -4

a)

no solution

b)

(0,0)

c)

infinite solutions

d)

(4,0)

31.

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

32.

How many solutions are there in the system of equations?

a)

No Solution

b)

Infinitely Many Solutions

c)

One Solution

d)

Two Solutions

33.

What is the number of solutions to the system of equations?

a)

No Solution

b)

Infinitely Many Solutions

c)

One Solution

d)

Two Solutions

34.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

35.

What is the solution to the system of equations?

a)

(-1, 1)

b)

(3, 1)

c)

(1, 1)

d)

(-3, 1)

36.

What would be the first step in finding the solution using elimination?

2x + 2y = -2

3x - 2y = 12

a)

you cannot solve this using eliminiation

b)

cross out the 2x and 3x, because when you add them, they equal 0

c)

cross out the 2y and -2y because when you add them, they equal 0

d)

change to slope intercept form and graph

37.

4x + 8y = 20

-4x + 2y = -30

When you solve these equations using the elimination method, which variable will be eliminated?

a)

The x

b)

The y

c)

The z

d)

The unknown

38.

The coefficients of the eliminated variable must be _____.

a)

opposites

b)

the same

c)

distinct

d)

does not matter

39.

When solving for $y$ , the coefficients of __ need to be opposites.

a)

$x$

b)

$y$

c)

$x$ and $y$

40.

When solving for $x$ , the coefficients of __ need to be opposites.

a)

$x$

b)

$y$

c)

$x$ and $y$

41.

Look for ____ when determining which variable to eliminate. Select all that apply

a)

same coefficeints with opposite signs

b)

easy numbers to multiply to (common factors)

c)

different coefficients

d)

vertical alignment of like terms

42.

To find the second variable, substitute the x or y you solved for into one of the ____.

a)

original equations

b)

one of the manipulated equations

c)

the top equation, always

d)

the bottom equation, always

43.

Order the algorithm (steps) to elimination

a)

Align like terms vertically

b)

Determine the variable to eliminate

c)

multiply equation(s) to have opposite coefficients, if necessary

d)

add vertically

e)

Solve for variable

1)

2)

3)

4)

5)

44.

Let's multiply the top equation by -2. What would be our new equation?

2x + 3y = 12

4x - 7y = - 54

a)

4x - 6y = -24

b)

-4x - 6y = 12

c)

-4x - 6y = 24

d)

-4x - 6y = -24

45.

-4x - 6y = -24

4x - 7y = - 54

Let's combine (add) these 2 equations to ELIMINATE the x variable. What would our combined equations be?

a)

-1y = 30

b)

13y = -30

c)

-1y = -78

d)

-13y = -78

46.

5x + y = 9
10x − 7y = −18

a)

(4, -11)

b)

(1, 4)

c)

(-1, 14)

d)

(-4, 29)

47.

Solve the system by elimination.

−6x + 6y = 0
9x − 8y = 4

a)

(4, −9)

b)

Infinite number of solutions

c)

(−9, 4)

d)

(4, 4)

48.

8x + 14y = 4
-6x - 7y = -10

a)

(4, -2)

b)

(-2, 4)

c)

(0, 3)

d)

(-4, -2)

49.

-x - 7y = 14
-4x - 14y = 28

a)

(-2, 0)

b)

(0, -2)

c)

(-2, -2)

d)

(0, 2)

50.

If two lines are parallel how many solutions do they have?

a)

1

b)

2

c)

infinite

d)

none

51.

Will the solution (-3, -7) make the following system of equations a true statement?
y = 4x + 5
y = x – 4

a)

YES

b)

NO

52.

Solve by elimination
4x-6y= -6
-2x-12y= -12

a)

(0,1)

b)

(1,0)

c)

(1,1)

d)

(2,1)

53.

Solve the system by elimination.

4x + 12y = −1
−3x − 9y = 0

a)

(10, 1)

b)

(−10, −1)

c)

(10, −1)

d)

No solution

54.

What is the solution to the system?

a)

(0, 3)

b)

(1, -1)

c)

(-3, 1)

d)

(1, 3)

55.

Solve by elimination
-12x-4y= -8
-6x-2y= -4

a)

no solution

b)

(0,0)

c)

infinite solutions

d)

(4,0)

56.

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

57.

How many solutions are there in the system of equations?

a)

No Solution

b)

Infinitely Many Solutions

c)

One Solution

d)

Two Solutions

58.

What is the number of solutions to the system of equations?

a)

No Solution

b)

Infinitely Many Solutions

c)

One Solution

d)

Two Solutions

59.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

60.

What is the solution to the system of equations?

a)

(-1, 1)

b)

(3, 1)

c)

(1, 1)

d)

(-3, 1)

61.

Type the solution to the system of equations as an ordered pair, (x,y).

(a)

62.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

63.

An ordered pair that satisfies both equations in a system of linear equations is called a (a) to the system of equations.

Choose from the below words

solution

coordinate

inconsistent

input

64.

Solve for x and y using substitution

y = 2x + 1

y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

65.

The solution of a system of linear equations is...

a)

the y-intercept (b)

b)

the intersection of the two equations on a graph

c)

the second equations' answers

d)

the slope (m)

66.

Solve by substitution:

y = 3x + 14

y = -4x

Type your answer as (x, y)

(a)

67.

Which problem would be easier to solve by substitution?

a)

y + x = 3

2y + x = 6

b)

3y - x = 7

2y = x + 6

c)

5x - 2y = 6

x + y = 2

d)

y = 2x + 2

x + y = 7

68.

Reorder the following steps for solving systems of linear equations by substitution

a)

Locate the isolated variable (nickname)

b)

Plug the solution into the original equation (nickname)

c)

Use the "nickname" in the other equation

d)

Plug the answer into the either equation to solve for the other variable

1)

2)

3)

4)

69.

Solve:
y = -1x - 5
4x - 8y = 4

a)

(-3, -2)

b)

(5, -7)

c)

(3, 9)

d)

(-5, 4)

70.

Solve:
y = 7x + 9
2y + 2x = -18

a)

(5, 0)

b)

(9, 18)

c)

(-2, -5)

d)

(1, 16)

71.

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)

72.

Solve:
x = -3y - 17
2x + 3y = -7

a)

(1, -20)

b)

(3, 0)

c)

(-5, -2)

d)

(10 , -9)

73.

Solve:
y=8x+1
y=6x+3

a)

(1, 9)

b)

(4, 14)

c)

(0, 1)

d)

(2, 4)

74.

Solve:
y = 4x - 10
y = 3x - 5

a)

(7 , -15)

b)

(1, -5)

c)

(5 , 10)

d)

(1, 2)

75.

What is the solution to this system?
y= 4x + 3
2x - 3y = 21

a)

(3,-9)

b)

(-3,-9)

c)

(-3,9)

d)

(0,1)

76.

What is the solution to this system?
y = x + 5
4x + y = 20

a)

(3,8)

b)

(8,3)

c)

(0,2)

d)

(2,0)

77.

What is the solution to this system?
y = 2x + 1
y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

78.

What is the solution to this system?
y = 4x + 1
3x + 2y = 13

a)

(1, 5)

b)

(5, 1)

c)

(0.25, 2)

d)

(-1,5)

79.

What is the solution to the system of equations?
y = 3x - 8
y = 4 - x

a)

(3,1)

b)

(1,3)

c)

(-3,1)

d)

(3,-1)

80.

What is the solution to the system?
2x - 2y = 2
y = -5x + 14

a)

(4, 5)

b)

(2.5, 1.5)

c)

(1.5, 5)

d)

(1, 2.25)

81.

^{What is the solution?}

a)

1

b)

-2

c)

(1, 2)

d)

(1, -1)

82.

Solve the following systems of equations using substitution:

y = 8

y = -4x + 4

a)

(8, -1)

b)

(-28, 8)

c)

(-1, 8)

d)

(8, -28)

83.

Solve the following systems of equations using substitution:

x = 6

y = 2x - 3

a)

(6, 6)

b)

(6, 9)

c)

(9, 6)

d)

(9, 9)

84.

How many solutions does the graph have?

a)

One solution

b)

No solution

c)

Infinite solutions

85.

Solve the following systems of equations using substitution:

y = 3 - x

3y + x = 5

a)

No solution

b)

(1, 2)

c)

(3, 0)

d)

(2, 1)

86.

The first step in solving using the substitution method is __________.

a)

get x by itself

b)

get y by itself

c)

get either variable by itself

d)

add the equations together

87.

Solve the following systems of equations using substitution:

2y + x = -15

x = 3y

a)

(-3, -9)

b)

(-9, -3)

c)

(-3, 9)

d)

(9, -3)

88.

What is the solution to this system?
y = x + 5
4x + y = 20

a)

(3,8)

b)

(8,3)

c)

(0,2)

d)

(2,0)

89.

Warm up: #3

Match the solution to the system of equations.

a)

1.

(-2, -1)

b)

2.

(2, -1)

c)

3.

(1, 4)

d)

4.

(-4, -1)

90.

Solve the following system:

y=6x-11

-2x-3y=-7

a)

$\left(2,\ 1\right)$

b)

$\left(1,\ 3\right)$

c)

$\left(2,\ 5\right)$

d)

$\left(3,\ 2\right)$

91.

y = 2x + 9

x = -3

a)

(-3, -33)

b)

(-3, 8)

c)

(-3, 3)

d)

(3, -3)

92.

6x = y

3y - 4x = 42

a)

(3, 18)

b)

(8, 2)

c)

(2, 8)

d)

(1, 6)

93.

y = 2x - 4

7x - 2y = 5

a)

(-1, -6)

b)

(-1, -8)

c)

(-2, 6)

d)

(1, -8),

94.

Solve:
y=8x+1
y=6x+3

a)

(1, 9)

b)

(4, 14)

c)

(0, 1)

d)

(2, 4)

95.

Find the solution of the system of equations below using the substitution method:

y = 2x - 4

7x - 2y = 5

a)

(-1, -6)

b)

(-1, -8)

c)

(-2, 6)

d)

(1, -8),

96.

Solve the system of equations.

a)

(-6, 1)

b)

(-12, -12)

c)

(1, -6)

d)

No solution

e)

Infinite solutions

97.

a)

No Solution

b)

(2, 2)

c)

(-1, 2)

d)

(-1, -2)

98.

y = 2x - 1
4x + y = 17

a)

(5, 3)

b)

(3, 5)

c)

(2, 5)

d)

(5, 2)

99.

y = -2x + 5
y = 2x - 11

a)

No Solution

b)

(0, 0)

c)

(3, -1)

d)

(4, -3)

100.

What is the solution to this system?
2x + 3y = 4
y= 5x - 27

a)

(5,-2)

b)

(5, 2)

c)

(2,3)

d)

(3,2)

101.

Solve the system by substitution.

5x + 4y= −14
y = −7x − 15

a)

(-2, -1)

b)

(1, -2)

c)

(-2, 1)

d)

(-1, -2)

102.

x - 3y = -13
4x + 2y = 4

a)

(1, 4)

b)

(-1, -4)

c)

(-1, 4)

d)

(1, -4)

103.

3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

104.

3x + 2y = 8
-x + y = -11

a)

(-5,6)

b)

(6,-11)

c)

(-6,-5)

d)

(6,-5)

105.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

intersecting lines

106.

7x - 5y = -24
-9x + 5y = 18

a)

(3, 9)

b)

(-3, -5/3)

c)

(3, 11)

d)

(3, -11)

107.

Solve:
x = -3y - 17
2x + 3y = -7

a)

(1, -20)

b)

(3, 0)

c)

(-5, -2)

d)

(10 , -9)

108.

y = -3x + 11
y = -6x - 13

a)

(-8, 35)

b)

(8, -13)

c)

(1, 8)

d)

(2, 13)

109.

3x + 2y = 8

-x + y = -11

a)

(-5,6)

b)

(6,-11)

c)

(-6,-5)

d)

(6,-5)

110.

Solve this system of equations.
y = 2x + 1
y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

111.

Solve by elimination:

4x\ +\ 9y\ =\ 28

-4x-1y\ =-28

a)

(-7,0)

b)

(6,0)

c)

(-6,0)

d)

(7,0)

112.

Solve by elimination:
$-9x-4y=-20$
$5x\ +\ 4y\ =\ 4$

a)

(-4,4)

b)

(4,4)

c)

(4,-4)

d)

(-4,-4)

113.

Solve by elimination:
$7x+1y=-9$
$-3x-1y=5$

a)

No solution

b)

(1,8)

c)

(-2,-3)

d)

(-1,-2)

114.

Is (-3, -7) a solution the system:

y = 4x + 5

y = x – 4

a)

YES

b)

NO

115.

Solve the system:
$3x+1y=19$
$2x-1y=6$

a)

(5, 14)

b)

(4, 5)

c)

(5, 4)

d)

(14, 5)

116.

Check to see if (-2,1) is a solution to the following system:

x + 2y = 0

4x + 3y = 1

a)

YES

b)

NO

117.

Is (1,10) a solution to the system:

y = 7x + 5

y = x + 9

a)

YES

b)

NO

118.

Is (1,7) a solution to the system:

y = 3x + 4

y = x + 6

a)

YES

b)

NO

119.

Is (0,2) a solution to the system:

3x + 2y = 4

8x - 3y = -6

a)

YES

b)

NO

120.

Is (5, 2) a solution to the system:

x + y = 7

x - y = 4

a)

YES

b)

NO

121.

Solve by elimination.

$3x+y=-1$

$4x-y=-13$

a)

(2 , 5)

b)

(-2 , 5)

c)

(2 , -7)

d)

(-2 , -7)

122.

Solve by elimination.

$4x+5y=5$

$4x+3y=11$

a)

(-5 , -3)

b)

(-5 , 3)

c)

(5 , -3)

d)

(5 , 3)

123.

Solve by elimination.

$2x+4y=-8$

$4x+5y=-1$

a)

(6 , 5)

b)

(6 , -5)

c)

(5 , 6)

d)

(5 , -6)

124.

Four times a number minus three times another number is thirteen. The sum of the two numbers is twelve. What are the two numbers? Use a system of equations to solve the problem.

a)

3 and 9

b)

-3 and 15

c)

5 and 7

d)

-5 and 17

125.

Bailey and Chloe went to the fair. Bailey bought two hotdogs and a soda for $5.50. Chloe bought a hotdog and two sodas for $5.00. Find the cost of a hotdog and the cost of a soda. Use a system of equations to solve the problem.

a)

hotdog: $2.50

soda: $1.00

b)

hotdog: $1.00

soda: $2.50

c)

hotdog: $1.50

soda: $2.00

d)

hotdog: $2.00

soda: $1.50

Solving Systems Substitution/Elimination Test

Total questions: 125

Worksheet time: 11hrs 40mins

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