WorksheetsSystems of Equations Review
Total questions: 115
Worksheet time: 14hrs 5mins
Name
Class
Date
1.
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
2.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(0, 1)
3.
How many solutions does this system of equations have?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
d)
Two Solutions
4.
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
5.
Solve the system of equations.
y = 4x+1
3x + 2y = 13
y = 4x+1
3x + 2y = 13
a)
(1, 5)
b)
(5, 1)
c)
(0.25, 2)
d)
∅
6.
Solve the system of equations by elimination.
-x + y = -13
-8x - 4y = -8
-x + y = -13
-8x - 4y = -8
a)
(5, 8)
b)
(5, -8)
c)
(-5, -18)
d)
(-5, 8)
7.
Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7
y = -x + 5
y = 2x - 7
a)
yes
b)
no
8.
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
2x + 4y = 450
b)
3x + 2y = 450
2x + 4y = 315
2x + 4y = 315
c)
2x + 2y = 315
3x + 4y = 450
3x + 4y = 450
9.
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
3x + 2y = 315
2x + 4y = 450
a)
45 minutes
b)
90 minutes
2x + 4y = 315
2x + 4y = 315
c)
60 minutes
3x + 4y = 450
3x + 4y = 450
d)
30 minutes
10.
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
y = 8.40 + x
b)
y = 9.65x + 43
y = 8.40x + 58
y = 8.40x + 58
c)
y =9.65x
y = 8.40x
y = 8.40x
d)
y = 9.65x - 43
y = 8.40x - 58
y = 8.40x - 58
11.
Solve for x and y.
y = 2/3x - 2
y = -x + 3
y = 2/3x - 2
y = -x + 3
a)
(0,3)
b)
(0,-3)
c)
(3,0)
d)
(-3,0)
12.
Solve for x and y
3x + 2y = 16
7x + y = 19
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
13.
7x+4y =12
x + 2y = -4
x + 2y = -4
a)
(-4,4)
b)
(4,4)
c)
(4,-4)
d)
(-4,-4)
14.
x + 2y = -4
x - 2y = 8
x - 2y = 8
a)
(2,5)
b)
(2,-3)
c)
(2,-2)
d)
(-3,2)
15.
7x - 2y = 6
x - 2y = -6
x - 2y = -6
a)
(2,4)
b)
(3,-2)
c)
(1,2)
d)
(-2,-4)
16.
x-4y = 16
5x + 4y = 8
5x + 4y = 8
a)
(4,-3)
b)
(-3,4)
c)
(4,3)
d)
(3,-4)
17.
5x - 2y = 6
x - 2y = -2
x - 2y = -2
a)
(2,2)
b)
(2,1)
c)
(1,2)
d)
(-2,-2)
18.
x + y = 3
3x - y = 1
3x - y = 1
a)
(2,1)
b)
(-1,2)
c)
(1,2)
d)
(-2,-1)
19.
x -2y = -2
3x - 2y = 6
3x - 2y = 6
a)
(4,3)
b)
(-3,4)
c)
(-2,-3)
d)
(-3,-4)
20.
3x - 2y = -8
5x + 2y = -8
5x + 2y = -8
a)
(1,-4)
b)
(-1,-4)
c)
(-4,1)
d)
(-2,1)
21.
x - 4y = -4
x + 2y = 8
x + 2y = 8
a)
(2,2)
b)
(4,2)
c)
(2,-2)
d)
(4,-2)
22.
x - 2y = 4
3x +2y = 4
3x +2y = 4
a)
(-2,-1)
b)
(4,-1)
c)
(2,-1)
d)
(4,1)
23.
x - 2y = 4
2x -y = -1
2x -y = -1
a)
(-2,-3)
b)
(-3,-2)
c)
(2,3)
d)
(3,2)
24.
5x + 3y = 6
x - 3y = 12
x - 3y = 12
a)
(3,3)
b)
(-3,-3)
c)
(3,-3)
d)
(3,-2)
25.
x - y = -2
y = -2
y = -2
a)
(1,-2)
b)
(-1,-2)
c)
(-4,-2)
d)
(4,-2)
26.
2x - 3y = 6
7x - 3y = -9
7x - 3y = -9
a)
(3,4)
b)
(4,-3)
c)
(-4,-3)
d)
(-3,-4)
27.
3x + y = 4
x + 2y = -2
x + 2y = -2
a)
(2,2)
b)
(-2,-2)
c)
(2,-2)
d)
(-2,2)
28.
2x + y = -3
x - 2y = -4
x - 2y = -4
a)
(-2,1)
b)
(1,-2)
c)
(2,1)
d)
(1,2)
29.
x = - 3
2x + 3y = 6
2x + 3y = 6
a)
(4,3)
b)
(-4,3)
c)
(-3,4)
d)
(3,-4)
30.
x + 4y = -8
5x - 4y = -16
5x - 4y = -16
a)
(4,1)
b)
(1,4)
c)
(-4,-1)
d)
(-1,-4)
31.
2x - 3y = 6
7x - 3y = -9
7x - 3y = -9
a)
(-3,-4)
b)
(3,4)
c)
(-4,-3)
d)
(4,3)
32.
5x - 4y = =-16
x+ 2y = -6
x+ 2y = -6
a)
(-4,-1)
b)
(5,-1)
c)
(-5,-1)
d)
(4,1)
33.
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.
34.
Determine how many solutions the system has.
a)
One Solution
b)
No Solutions
c)
Infinitely Many Solutions
d)
Mikey is my friend.
35.
Determine how many solutions the system has.
(Hint: Both lines are graphed over each other)
(Hint: Both lines are graphed over each other)
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
d)
I am Spartacus!
36.
Determine how many solutions this system has.
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
d)
What is a solution?
37.
Which of the following is NOT a method to solve systems?
a)
Elimination
b)
Distribution
c)
Substitution
d)
Graphing
38.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
39.
Solve the system of equations
4x+8y=20
-4x+2y=-30
4x+8y=20
-4x+2y=-30
a)
(-7,1)
b)
(2,-5)
c)
(-2,5)
d)
(7,-1)
40.
Where do these lines intersect?
x-y=11
2x+y=19
x-y=11
2x+y=19
a)
(10,-1)
b)
(-1,10)
c)
(3,-4)
d)
(6,7)
41.
Solve for x and solve for y
3x - 3y = 33
6x - 3y = 57
3x - 3y = 33
6x - 3y = 57
a)
(8,-3)
b)
(-3,8)
c)
(10,1)
d)
(10,-1)
42.
Solve the system using elimination.
3x + 2y = 16
7x + y = 19
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
43.
Solve for x and y
y = 2x + 1
y = 4x - 1
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
44.
Alex and Billy are running laps. According to the graph, how long will it take for the two boys to run the same distance?
a)
20 minutes
b)
15 minutes
c)
10 minutes
d)
5 minutes
45.
Solve using elimination.
4x + 8y = 20
-4x + 2y = -30
4x + 8y = 20
-4x + 2y = -30
a)
(-7,1)
b)
(2,-5)
c)
(-2,5)
d)
(7,-1)
46.
Solve the system by elimination.
−8x − 10y = 20
−8x − 6y = −4
−8x − 10y = 20
−8x − 6y = −4
a)
Infinite number of solutions
b)
(6, 5)
c)
(−6, −5)
d)
(5, −6)
47.
Solve by elimination:
9x-4y=7
x-4y=-17
9x-4y=7
x-4y=-17
a)
(-1,5)
b)
(-7,5)
c)
(7,5)
d)
(3,5)
48.
-4x - 6y = 6
4x + 6y = -4
4x + 6y = -4
a)
no solution
b)
(2,0)
c)
(-4,0)
d)
(0,0)
49.
Solve the system of Equation (x,y)
3x + 2y = –13
3x + 4y = 1
3x + 2y = –13
3x + 4y = 1
a)
(-9,7)
b)
(7,-9)
c)
(4,-7)
d)
(-7,-4)
50.
5x + 16y = -16
-9x - 8y = 8
-9x - 8y = 8
a)
(3, 1)
b)
(3, -1)
c)
(-3, -1)
d)
(0, -1)
51.
Solve for x and y
3x + 2y = 16
7x + y = 19
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
52.
Solve the system of Equation (x,y)
−4x + 9y = 9
x − 3y = −6
−4x + 9y = 9
x − 3y = −6
a)
(-9,-5)
b)
(-5,9)
c)
(9,5)
d)
(-5,-9)
53.
Solve the system by elimination.
12x + 36y = −3
−12x − 36y = 0
12x + 36y = −3
−12x − 36y = 0
a)
(10, 1)
b)
(−10, −1)
c)
(10, −1)
d)
No solution
54.
Solve by elimination
-6x + 5y = 1
6x + 4y = -10
-6x + 5y = 1
6x + 4y = -10
a)
(1,-1)
b)
(0,-1)
c)
(1,1)
d)
(-1,-1)
55.
Solve by elimination:
4x+9y=28
-4x-y=-28
4x+9y=28
-4x-y=-28
a)
(-7,0)
b)
(6,0)
c)
(-6,0)
d)
(7,0)
56.
-4x - 6y = 6
4x + 6y = -4
4x + 6y = -4
a)
no solution
b)
(2,0)
c)
(-4,0)
d)
(0,0)
57.
Solve by elimination:
3x+7y=23
-3x-7y=-17
3x+7y=23
-3x-7y=-17
a)
No solution
b)
ARN
c)
(-3,3)
d)
(3,3)
58.
Solve the system by elimination.
−4x − 4y = 0
4x + 4y = 0
−4x − 4y = 0
4x + 4y = 0
a)
(−6, −4)
b)
Infinite number of solutions
c)
(−6, 10)
d)
(6, 4)
59.
Solve by elimination:
7x-9y=29
7x+2y=-15
7x-9y=29
7x+2y=-15
a)
(-4,-1)
b)
(-1.-4)
c)
(-1,4)
d)
(-1,6)
60.
Solve the system by elimination.
−8x − 10y = 20
−8x − 6y = −4
−8x − 10y = 20
−8x − 6y = −4
a)
Infinite number of solutions
b)
(6, 5)
c)
(−6, −5)
d)
(5, −6)
61.
-4x-2y=-12
4x+8y=-24
4x+8y=-24
a)
(5,6)
b)
(6,-6)
c)
(6,-2)
d)
(4,-3)
62.
Solve using elimination.
7x + 2y = 24
8x + 2y = 30
7x + 2y = 24
8x + 2y = 30
a)
(6,-9)
b)
(-9,6)
c)
No solution
d)
Infinite number of solutions
63.
Solve by elimination:
4x + 4y = 4
3x + 4y =10
4x + 4y = 4
3x + 4y =10
a)
(7,-6)
b)
(-6,7)
c)
(6,7)
d)
(7,6)
64.
Solve by elimination:
3x + 7y = 23
-3x - 7y = -17
3x + 7y = 23
-3x - 7y = -17
a)
No solution
b)
Infinite number of solutions
c)
(-3,3)
d)
(3,3)
65.
Solve the system by elimination.
5x + 8y = -12
3x + 5y = -7
5x + 8y = -12
3x + 5y = -7
a)
(1, -10)
b)
No solution
c)
(-4, 1)
d)
(1, 10)
66.
x-y=11
2x+y=19
2x+y=19
a)
(10,-1)
b)
(-1,10)
c)
(3,-4)
d)
(6,7)
67.
What is the solution?
a)
1
b)
-2
c)
(1, 2)
d)
(1, -1)
68.
This system has _____ solutions
a)
no
b)
1
c)
2
d)
Infinitely many
69.
What is the solution?
(Hint: Both lines are graphed over each other)
(Hint: Both lines are graphed over each other)
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
70.
What is the solution to the system?
a)
(3, -1)
b)
(2, -6)
c)
No Solution
d)
(6, -2)
71.
Steffen graphed two lines in order to find the solution to a given system of equations.
What is the solution?
What is the solution?
a)
(-3,-8)
b)
(-8,-3)
c)
(3,-8)
d)
(8,3)
72.
a)
(2, -2)
b)
(2, 2)
c)
(-2, 2)
d)
(-2, -2)
73.
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.
74.
Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3
8x + 4y = 12
y = -2x + 3
a)
(0,3)
b)
(3,0)
c)
No solution(parallel lines)
d)
Infinitely many solutions
75.
2x - y = 0
4x - y = 0
a)
(1,2)
b)
(0,0)
c)
No Solutions
d)
Infinite Solutions
76.
Solve for x and y.
y = 2/3x - 2
y = -x + 3
y = 2/3x - 2
y = -x + 3
a)
(0,3)
b)
(0,-3)
c)
(3,0)
d)
(-3,0)
77.
Solve for x and y
3x + 2y = 16
7x + y = 19
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
78.
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?
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
79.
What is the value of the y-coordinate of the solution to the system of equations
x-2y=1
x+4y=7
x-2y=1
x+4y=7
a)
1
b)
-1
c)
3
d)
4
80.
Solve the following system by setting the two equations equal to each other. What is the solution?
HINT: - 1/3x + 4 = 2/3x + 1 and then solve for x. Once you find x go back and find y.
HINT: - 1/3x + 4 = 2/3x + 1 and then solve for x. Once you find x go back and find y.
a)
Infinite number of solutions
b)
(3, 3)
c)
(3, -3)
d)
(-3, 3)
81.
Solve:
3x + 2y = 16
7x + y = 19
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
82.
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
2s + 3c = 52
b)
3s + 1c = 38
3s + 2c = 52
3s + 2c = 52
c)
s + c = 38
s + c = 52
s + c = 52
d)
3s + 3c = 38
1s + 2c = 52
1s + 2c = 52
83.
Solve:
y = 8x + 2
y = -x - 7
y = 8x + 2
y = -x - 7
a)
(1, 10)
b)
(-1, -6)
c)
(2, 7)
d)
(9, 9)
84.
Solve:
6x + 2y = -20
y = -2x - 4
6x + 2y = -20
y = -2x - 4
a)
(-5, -14)
b)
(1, 6)
c)
(-6, 8)
d)
(2, -8)
85.
Solve:
y = 4x - 10
y = 3x - 5
y = 4x - 10
y = 3x - 5
a)
(7 , -15)
b)
(1, -5)
c)
(5 , 10)
d)
(1, 2)
86.
What is the solution?
a)
1
b)
-2
c)
(1, 2)
d)
(1, -1)
87.
This system has _____ solutions
a)
no
b)
1
c)
2
d)
Infinitely many
88.
What is the solution?
(Hint: Both lines are graphed over each other)
(Hint: Both lines are graphed over each other)
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
89.
What is the solution to the system?
a)
(3, -1)
b)
(2, -6)
c)
No Solution
d)
(6, -2)
90.
Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3
8x + 4y = 12
y = -2x + 3
a)
(0,3)
b)
(3,0)
c)
No solution(parallel lines)
d)
Infinitely many solutions
91.
Solve for x and y
3x + 2y = 16
7x + y = 19
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
92.
What is the value of the y-coordinate of the solution to the system of equations
x-2y=1
x+4y=7
x-2y=1
x+4y=7
a)
1
b)
-1
c)
3
d)
4
93.
x-y=11
2x+y=19
2x+y=19
a)
(10,-1)
b)
(-1,10)
c)
(3,-4)
d)
(6,7)
94.
Solve the system by substitution.
-5x - 4y = -9
y = 6
-5x - 4y = -9
y = 6
a)
(3, 6)
b)
(6, -3)
c)
(-3, 6)
d)
(6.8, 3)
95.
Solve the system by substitution.
y = 2x − 11
2x − 8y = 4
y = 2x − 11
2x − 8y = 4
a)
(6, 1)
b)
(6, −4)
c)
(6, −1)
d)
Infinite number of solutions
96.
Solve:
y = -1x - 5
4x - 8y = 4
y = -1x - 5
4x - 8y = 4
a)
(-3, -2)
b)
(5, -7)
c)
(3, 9)
d)
(-5, 4)
97.
How many solutions will this system have?
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
98.
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
99.
Solve:
y=8x+1
y=6x+3
y=8x+1
y=6x+3
a)
(1, 9)
b)
(4, 14)
c)
(0, 1)
d)
(2, 4)
100.
y = 3x + 9
y = -6
y = -6
a)
( -7 , 6 )
b)
( 1 , -6 )
c)
( 7 , -6 )
d)
( -5 , -6 )
101.
Solve the system of equations.
y = 4x + 1
3x + 2y = 13
a)
(1, 5)
b)
(5, 1)
c)
(0.25, 2)
d)
∅
102.
- 3x + y = -8
x + y = 4
x + y = 4
a)
(3, 1)
b)
(1, 3)
c)
(3, -1)
d)
(-3, 1)
103.
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)
104.
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
105.
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)
106.
Solve the system of equations.
a)
(10, 3)
b)
(6, 3)
c)
(15, 3)
d)
No solution
e)
Infinite Solution
107.
Solve the system of equations.
a)
(11, 21)
b)
(3, 11)
c)
(11, -67)
d)
No solution
e)
Infinite solutions
108.
Solve the system of equations.
a)
(-7, 8)
b)
(-7, -6)
c)
(8, -7)
d)
No solution
e)
Infinite solutions
109.
Solve the system of equations.
a)
(-6, 30)
b)
(-2, 10)
c)
(44, 39)
d)
No solution
e)
Infinite solutions
110.
Solve the system of equations.
a)
(-6, 1)
b)
(0, 0)
c)
(1, -6)
d)
No solution
e)
Infinite solutions
111.
Solve the system of equations.
a)
(3, 33)
b)
(7, 77)
c)
(2, 22)
d)
No solution
e)
Infinite solutions
112.
Which graph represents a system of equations with infinite solutions?
a)
b)
c)
d)
None of the above
113.
Which graph represents a system of equations with no solution?
a)
b)
c)
d)
None of the above
114.
Solve the system of equations
a)
(1, -4)
b)
(1, 4)
c)
(-4, -7)
d)
(-7, -4)
115.
Solve the system of equations.
a)
(-34, -17)
b)
(8, 4)
c)
(10, 20)
d)
No solution
e)
Infinite solutions
100 %
