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Solve System of Linear Equation by graphing, elimination, substitution

Total questions: 70

Worksheet time: 1hrs 10mins

Name
Class
Date
1.
What is the solution? 
a)
1
b)
-2
c)
(1, 2)
d)
(1, -1)
2.
Solve using elimination. 
 −4x − 4y = 0
4x + 4y = 0 
a)
(−6, −4) 
b)
Infinite number of solutions  
c)
(−6, 10) 
d)
(6, 4) 
3.
Solve using elimination.
-4x - 6y = 6
4x + 6y = -4
a)
no solution
b)
(2,0)
c)
(-4,0)
d)
(0,0)
4.
Solve the system given:
3x - y = 7
2x + y = 3
a)
(-1,2)
b)
(5,4)
c)
(4,5)
d)
(2,-1)
5.
The solution (x, y) to a system of equations is the point where they...? 
a)
Run off the graph
b)
Don't touch
c)
Intersect
d)
Exist
6.
Parallel Lines never intersect because...
a)
they have the same slopes. 
b)
they have the same y-intercept.
c)
they have different slopes.
d)
they have different y-intercepts. 
7.
This system has _____ solutions
a)
0
b)
1
c)
2
d)
Infinitely many
8.
What is the solution?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
9.
If the solution is infinitely many the lines will ________?
a)
intersect at exactly one point
b)
be parallel
c)
overlap each other
d)
never exist
10.
The solution to a system of equations is any ordered pair that makes both equations true. 
a)
TRUE
b)
FALSE
11.

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)

12.

What variable do you eliminate?


4x + 8y = 20

−4x + 2y = −30

a)

X because they have opposite signs

b)

Y because they have opposite signs

13.

You can solve systems using these methods:

a)

graphing, substitution, and elimination

b)

rearranging, thinking, and guessing

c)

only by graphing

14.

Solve the following system:

y=−2y=-2  

4x−3y=184x-3y=18  

a)

(3, −2)\left(3,\ -2\right)  

b)

(3, 2)\left(3,\ 2\right)  

c)

(−2,3)\left(-2,3\right)  

d)

(2, 3)\left(2,\ 3\right)  

15.

Solve this system by substitution.

a)

(1, -4)

b)

(1, 4)

c)

(-4, -7)

d)

(-7, -4)

16.

What variable do you eliminate, and what do you multiply the equation(s) by?

5x + y = 9

10x − 7y = −18

a)

You eliminate x, and multiply the top equation by 11

b)

You eliminate y, and multiply the top equation by 7

17.
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)
18.
Which of the following are ways to solve systems of equations? 
a)
Graphing
b)
Substitution
c)
Elimination
d)
All of the above
19.
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)
20.
Solve the system by elimination. 
 −4x − 4y = 0
4x + 4y = 0 
a)
(−6, −4) 
b)
Infinite number of solutions  
c)
(−6, 10) 
d)
(6, 4) 
21.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(0, 1)
22.
A system of linear equations is... 
a)
Math Magic
b)
One Equation
c)
Always more than 2 equations
d)
A set of 2 or more equations
23.
What is the solution?
a)
(6, 3)
b)
(3, 6)
c)
(-6, 3)
d)
No solution
24.
Solve by elimination:
3x+7y=23

-3x-7y=-17
a)
No solution
b)
ARN
c)
(-3,3)
d)
(3,3)
25.

Solve the following system using graphing. What is the solution?

a)

(3, -1)

b)

(-1, -3)

c)

(-1, -1)

d)

(-1, 3)

26.

Solve for x and y using substitution

y = 2/3x - 2

y = -x + 3

a)

(0,3)

b)

(0,-2)

c)

(3,0)

d)

(-3,0)

27.

Is the point (-2, 4) a solution to the system of equations shown below?


x – y = 6


2x + y = 0

a)

yes

b)

no

28.

When does a system of equations have no solutions?

a)

When the lines cross in only one point

b)

When lines are perpendicular

c)

When the lines are parallel

d)

There is ALWAYS a solution!

29.

Which variable will be eliminated first?

a)

x

b)

y

30.

Solve the system of equations using substitution

y = -6

-3x - 6y = 24

a)

(6, 6)

b)

(6, -6)

c)

(4, -6)

d)

(-6, 4)

31.
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
32.
If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 
a)
Intersecting lines
b)
Same line
c)
Parallel lines
33.
If a system of equations has no solution, what does the graph look like? 
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
same lines
34.

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, how many of each type of ticket were sold? What of the following systems represent this situation?

a)

S + A = 530

3S + 4A = 1740

b)

S + A = 530

4S + 3A = 1740

c)

S + A = 1740

3S + 4A = 530

d)

S + A = 1740

4S + 3A = 530

35.

Which method would be best (quickest) for solving the system below:

x + y = 11

3x - 4y = -2

a)

Making trials

b)

Elimination

c)

Graphing

d)

None of these

36.
Which method would be best (quickest) for solving the system below:
3x - 4y = -2
y = 2x + 1
a)
Substitution
b)
Elimination
c)
Graphing
d)
None
37.

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 cancel out.

d)

change to slope intercept form and graph

38.

Which choice shows substitution correctly?

x = 3y -7

2x + 4y = 9

a)

2x + 4(3y - 7) = 9

b)

2(3y -7) + 4y = 9

39.

A ________________ are two or more equations that have the same variables and work together.

a)

graphing lines

b)

elimination method

c)

system of equations

d)

table

40.

What is an important step in solving a system by Substitution?

a)

Make sure both equations are in standard form.

b)

Make sure at least one equation is solved for one variable.

c)

Make sure both equations are the same.

d)

Make sure both equations can be solved.

41.
Diego scores 11 more points than Travis.  Together they score 21 points.  How many points did each person score?
a)
Diego: 11,   Travis: 10
b)
Diego:  10,  Travis:  11
c)
Diego: 5,  Travis:  16
d)
Diego:  16, Travis:  5
42.

What would be the first step to solve this system by elimination?

2x+9y= -7

6x-3y= 9

a)

Add the equations

b)

Subtract the equations

c)

Write each equation in slope intercept form.

d)

Multiple the first equation by 3 or -3

43.

To eliminate the x-variable in the system of equations, multiply the second equation by which number?

a)

-3

b)

-2

c)

-1

d)

0

44.

Which strategy is the best choice for solving this system?

4x − 4y = 10

4x + 4y = 0

a)

Elimination

b)

Making trials

c)

Substitution

d)

Graphing

45.

Which strategy is the best choice for solving this system?

y = 7x

4x + 4y = 20

a)

Elimination

b)

Elimination with multiplication

c)

Substitution

d)

Graphing

46.
Which of the following is not a method to solve systems?
a)
Elimination
b)
Difference of Squares
c)
Substitution
d)
Graphing
47.
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
48.
What is the solution?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
d)
(0, -1.5)
49.
The ordered pair that satisfies all equations in the system.
a)
system of equations
b)
function
c)
graph
d)
solution of a system
50.
solve by substitution: y=3x+14
y=-4x
a)
y=3
b)
y=1
c)
y=2
d)
y=4
51.
Solve the system of equations by elimination.
-x + y = -13
-8x - 4y = -8 
a)
(5, 8)
b)
(5, -8)
c)
(-5, -18)
d)
(-5, 8)
52.
If a system of linear equations has one solution, what does this mean about the two lines? 
a)
Parallel lines
b)
the same line 
c)
Intersecting lines
53.
The number that is multiplied by the variable
a)
Idependent
b)
Dependent
c)
Coefficient 
d)
Parallel 
54.
What is the y-intercept of this graph?
a)
(0,1)
b)
(0,-2)
c)
(0,0)
d)
(0,3)
55.
There are 50 donkeys and chickens on a far.  There are a total of 174 legs.  Which system below can be used to figure out how many of each animal the farm has?
a)
d + c = 174
4d + 2c = 50
b)
d + c = 50
4d + 2c = 174
c)
d + c = 50
2d + 4c = 174
d)
d + c = 174
2d + 4c = 50
56.
What is the solution to the system?
a)
(3, -1)
b)
(2, -6)
c)
No Solution 
d)
(6, -2)
57.
Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3
a)
(0,3)
b)
(3,0)
c)
No solution(parallel lines)
d)
Infinitely many solutions
58.
Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7
a)
yes
b)
no
59.
Solve the system by elimination. 
 −4x − 4y = 0
4x + 4y = 0 
a)
(−6, −4) 
b)
Infinite number of solutions  
c)
(−6, 10) 
d)
(6, 4) 
60.

What is the best method do you use?

y = 6x − 11

−2x − 3y = −7

a)

Graphing

b)

Substitution because a variable is defined

c)

Elimination because both equations are in standard form.

61.

What variable do you eliminate?


4x + 8y = 20

−4x + 2y = −30

a)

X because they have opposite signs

b)

Y because they have opposite signs

62.

What is the proper set up to solve the equation?

-7x -2y= -13

x = 2y+11

a)

-7(11) -2y = -13

b)

-7(2y +11)-2y = -13

c)

-7x -2(11) =-13

d)

-7x - 2(2y+11)= -13

63.

What variable do you eliminate, and what do you multiply the equation(s) by?

5x + y = 9

10x − 7y = −18

a)

You eliminate x, and multiply the top equation by -2

b)

You eliminate y, and multiply the top equation by 7

64.

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)

65.
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
66.
The solution (x, y) to a system of equations is the point where they...? 
a)
Run off the graph
b)
Don't touch
c)
Intersect
d)
Exist
67.

Which is the best method to use?


y = 6x − 11

−2x − 3y = −7

a)

Graphing

b)

Substitution because a variable is isolated.

c)

Elimination because both equations are in standard form.

68.

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)

69.

Which method would be best (quickest) for solving the system below:

x + y = 11

3x - 4y = -2

a)

Substitution

b)

Elimination

c)

Graphing

d)

None of these

70.

Solve by elimination:

4x+9y=28

-4x-y=-28

a)

(-7,0)

b)

(6,0)

c)

(-6,0)

d)

(7,0)

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