WorksheetsSystems of Equations
Total questions: 92
Worksheet time: 8hrs 40mins
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.
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)
4.
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)
5.
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
6.
Solve the system given:
3x - y = 7
2x + y = 3
3x - y = 7
2x + y = 3
a)
(-1,2)
b)
(5,4)
c)
(4,5)
d)
(2,-1)
7.
Give the solution to the system.
a)
(3,1)
b)
(1,3)
c)
(-1,3)
d)
(1, -3)
8.
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
9.
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.
10.
David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?
a)
1.5x+0.5y=78.5
x+y=87
x+y=87
b)
1.5x+0.5y=78.5
1.5x+0.5y=87
1.5x+0.5y=87
c)
x+y=78.5
1.5x+0.5y=87
1.5x+0.5y=87
d)
x+y=78.5
x+y=87
x+y=87
11.
What is the solution to the system?
a)
(-1, 3)
b)
(-3, 1)
c)
(3, -1)
d)
(-3, -1)
12.
What is the number of solutions to the system of equations?
a)
No Solution
b)
Infinitely Many Solutions
c)
One Solution
d)
Two Solutions
13.
How many solutions are there in the system of equations?
a)
No Solution
b)
Infinitely Many Solutions
c)
One Solution
d)
Two Solutions
14.
What is the solution to the system of equations?
a)
No Solution
b)
(2, 0)
c)
Infinitely Many Solutions
d)
(0, 2)
15.
What is the solution to the system of equations?
a)
(-1, -3)
b)
(3, 1)
c)
(1, 3)
d)
(-3, -1)
16.
What is the solution to the system of equations?
a)
(2, -2)
b)
(2, 2)
c)
No Solution
d)
(-2, -2)
17.
What is the solution to the system of equations?
a)
(3, 4)
b)
(-3, -4)
c)
(-4, -3)
d)
(4, 3)
18.
What is the solution to the system of equations?
a)
(-3, 1)
b)
(1, -3)
c)
(3, -1)
d)
(-1, 3)
19.
What is the solution to the system of equations?
a)
No Solution
b)
Infinitely Many Solutions
c)
(7, -2)
d)
(-5, -5)
20.
What is the solution to the systems of equations?
a)
(-7, -9)
b)
(-10, 5)
c)
No Solution
d)
Infinitely Many Solutions
21.
What is the solution to this system?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
22.
When you graph the exact same equation twice,
a)
you will have no solution.
b)
you will have one solution.
c)
you will have infinite solutions.
d)
you will graph a giraffe.
23.
How many solutions will this system have?
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
24.
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
25.
What is the solution to the system?
a)
(3, -1)
b)
(2, -6)
c)
No Solution
d)
(6, -2)
26.
Solve by graphing.
y = 2x + 1
y = 4x - 1
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
27.
Solve this system of equations by graphing.
y = 1/2x + 2
y = -3x + 9
a)
(2, 3)
b)
(-2, -3)
c)
(3, 2)
d)
(-3, 2)
28.
Solve the following system by graphing. What is the solution?
a)
(-4, 2)
b)
(4, 2)
c)
(2, -4)
d)
(2, 4)
29.
Solve the following system by graphing. What is the solution?
a)
(3, -1)
b)
(-1, -3)
c)
(-1, -1)
d)
(-1, 3)
30.
Buzz graphed two lines in order to find the solution to a given system of equations.
What is the solution?
What is the solution?
a)
(-1, 4)
b)
(1, -4)
c)
(-4, 1)
d)
(4, -1)
31.
How many solutions will this system have?
a)
No Solution
b)
Infinitely Many Solutions
c)
No Clue
d)
One solution
32.
What is the solution?
a)
1
b)
-2
c)
(1, 2)
d)
(1, -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.
How many solutions will this system have?
a)
One
b)
Two
c)
No Solution
d)
Infinitely Many Solutions
35.
How many solutions will this system have?
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
36.
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
37.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
38.
What is the solution to the system?
a)
(3, -1)
b)
(2, -6)
c)
No Solution
d)
(6, -2)
39.
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
40.
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
41.
Alex 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)
(-8,-3)
d)
(8,3)
42.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
43.
Lesly 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)
44.
Solve the following system by graphing. What is the solution?
a)
Infinite number of solutions
b)
(3, 3)
c)
(3, -3)
d)
(-3, 3)
45.
What is the solution?
a)
(6, 3)
b)
(3, 6)
c)
(-6, 3)
d)
No solution
46.
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)
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.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
50.
Give the solution to the system.
a)
(3,1)
b)
(1,3)
c)
(-1,3)
d)
(1, -3)
51.
What is the solution to the system of equations?
y = 3x - 8
y = 4 - x
y = 3x - 8
y = 4 - x
a)
(3,1)
b)
(1,3)
c)
(-3,1)
d)
(3,-1)
52.
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
53.
The ordered pair that satisfies all equations in the system.
a)
system of equations
b)
function
c)
graph
d)
solution of a system
54.
Find the solution to the system.
y = x-6
y = -3x + 2
y = x-6
y = -3x + 2
a)
(0, -6)
b)
(6, 0)
c)
(-4, 2)
d)
(2, -4)
55.
What kind of lines have no solution to a system of equations
a)
Parallell Lines
b)
Overlapping lines
c)
Intersecting Lines
d)
Skew Lines
56.
7x+4y =12
x + 2y = -4
x + 2y = -4
a)
(-4,4)
b)
(4,4)
c)
(4,-4)
d)
(-4,-4)
57.
x + 2y = -4
x - 2y = 8
x - 2y = 8
a)
(2,5)
b)
(2,-3)
c)
(2,-2)
d)
(-3,2)
58.
7x - 2y = 6
x - 2y = -6
x - 2y = -6
a)
(2,4)
b)
(3,-2)
c)
(1,2)
d)
(-2,-4)
59.
x-4y = 16
5x + 4y = 8
5x + 4y = 8
a)
(4,-3)
b)
(-3,4)
c)
(4,3)
d)
(3,-4)
60.
5x - 2y = 6
x - 2y = -2
x - 2y = -2
a)
(2,2)
b)
(2,1)
c)
(1,2)
d)
(-2,-2)
61.
x + y = 3
3x - y = 1
3x - y = 1
a)
(2,1)
b)
(-1,2)
c)
(1,2)
d)
(-2,-1)
62.
x -2y = -2
3x - 2y = 6
3x - 2y = 6
a)
(4,3)
b)
(-3,4)
c)
(-2,-3)
d)
(-3,-4)
63.
3x - 2y = -8
5x + 2y = -8
5x + 2y = -8
a)
(1,-4)
b)
(-1,-4)
c)
(-4,1)
d)
(-2,1)
64.
x - 4y = -4
x + 2y = 8
x + 2y = 8
a)
(2,2)
b)
(4,2)
c)
(2,-2)
d)
(4,-2)
65.
x - 2y = 4
3x +2y = 4
3x +2y = 4
a)
(-2,-1)
b)
(4,-1)
c)
(2,-1)
d)
(4,1)
66.
x - 2y = 4
2x -y = -1
2x -y = -1
a)
(-2,-3)
b)
(-3,-2)
c)
(2,3)
d)
(3,2)
67.
5x + 3y = 6
x - 3y = 12
x - 3y = 12
a)
(3,3)
b)
(-3,-3)
c)
(3,-3)
d)
(3,-2)
68.
x - y = -2
y = -2
y = -2
a)
(1,-2)
b)
(-1,-2)
c)
(-4,-2)
d)
(4,-2)
69.
2x - 3y = 6
7x - 3y = -9
7x - 3y = -9
a)
(3,4)
b)
(4,-3)
c)
(-4,-3)
d)
(-3,-4)
70.
3x + y = 4
x + 2y = -2
x + 2y = -2
a)
(2,2)
b)
(-2,-2)
c)
(2,-2)
d)
(-2,2)
71.
2x + y = -3
x - 2y = -4
x - 2y = -4
a)
(-2,1)
b)
(1,-2)
c)
(2,1)
d)
(1,2)
72.
x = - 3
2x + 3y = 6
2x + 3y = 6
a)
(4,3)
b)
(-4,3)
c)
(-3,4)
d)
(3,-4)
73.
x + 4y = -8
5x - 4y = -16
5x - 4y = -16
a)
(4,1)
b)
(1,4)
c)
(-4,-1)
d)
(-1,-4)
74.
2x - 3y = 6
7x - 3y = -9
7x - 3y = -9
a)
(-3,-4)
b)
(3,4)
c)
(-4,-3)
d)
(4,3)
75.
5x - 4y = =-16
x+ 2y = -6
x+ 2y = -6
a)
(-4,-1)
b)
(5,-1)
c)
(-5,-1)
d)
(4,1)
76.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
77.
What is the solution?
a)
1
b)
-2
c)
(1, 2)
d)
(1, -1)
78.
What is the solution?
a)
(6, 3)
b)
(3, 6)
c)
(-6, 3)
d)
No solution
79.
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.
80.
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
81.
2x - y = 0
4x - y = 0
a)
(1,2)
b)
(0,0)
c)
No Solutions
d)
Infinite Solutions
82.
How many solutions?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
83.
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)
84.
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)
85.
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
86.
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
87.
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
88.
What is the solution?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
89.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
90.
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)
91.
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)
92.
Which of the following is not a method to solve systems?
a)
Elimination
b)
Difference of Squares
c)
Substitution
d)
Graphing
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