WorksheetsSolving Systems of Equations and Inequalities
Total questions: 28
Worksheet time: 3hrs 20mins
Name
Class
Date
1.
Solve the system of equations .
a)
(3, 6)
b)
No Solution
c)
(-3, 6)
d)
(6, 3)
2.
Find the solution to the system.
x − y = 3
7x − y = −3
x − y = 3
7x − y = −3
a)
(4, 1)
b)
(-1,-4)
c)
(-1,-1)
d)
( 1, 4)
3.
Find the solution to the system using substitution.
4x – 3y = 5
y = 2x – 3
4x – 3y = 5
y = 2x – 3
a)
(2,1)
b)
(1,2)
c)
(2,2)
d)
the answer is not listed
4.
What is the solution?
a)
(7, -2)
b)
(7,2)
c)
(2, 7)
d)
(-2, 7)
5.
Solve this system of equations by graphing or substitution.
y = 1/2x + 2
y = -3x + 9
y = 1/2x + 2
y = -3x + 9
a)
(2,3)
b)
(-2,-3)
c)
(3, 2)
d)
(-3,2)
6.
Solve the system of equations.
y = 2x + 1
y = 4x - 1
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
7.
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.
8.
How many solutions will this system have?
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
9.
Solve the system of equations.
y = 6x - 4
y = -x + 3
y = 6x - 4
y = -x + 3
a)
(1, 2)
b)
(2, 1)
c)
(4, 5)
d)
(2, 4)
10.
What is the solution to this system?
x = 7 - 2y
2x + y = 5
x = 7 - 2y
2x + y = 5
a)
(-1,4)
b)
(4,-1)
c)
(1,3)
d)
(3,1)
11.
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)
12.
Solve the following system using the method of your choice.
a)
(1, -5)
b)
(-5, 1)
c)
(-4, 1)
d)
No solution
13.
A gym charges a one-time registration fee as well as a monthly fee. The cost of joining the gym for 4 months is $370, and the cost of joining for 6 months is $530. Write a system of equations to find the registration fee and monthly fee. m= months; r = registration fee.
a)
r - 4m = 370
r - 6m = 530
r - 6m = 530
b)
r + 4m = 370
r + 6m = 530
r + 6m = 530
c)
m + 4r = 370
m + 6r = 530
m + 6r = 530
d)
m - 4r = 370
m - 6r = 530
m - 6r = 530
14.
Match the system to the graph (solution set is on the left)
a)
y ≤ 3x and y ≤ -2x + 4
b)
y > 3x and y > -2x + 4
c)
y < 3x and y > -2x + 4
d)
y > 3x and y < -2x + 4
15.
Match the system to the graph.
a)
y > -1/5x - 1/2 and y ≥ -2x - 4
b)
y > -1/5x - 1/2 and y ≤ -2x - 4
c)
y ≥ -1/5x - 1/2 and y ≤ -2x - 4
d)
y < -1/5x - 1/2 and y ≥ -2x - 4
16.
Match the system to the graph.
a)
y ≥ -x - 1 and y < x + 4
b)
y < -x - 1 and y ≥ x + 4
c)
y > -x - 1 and y ≥ x + 4
d)
y > -x - 1 and y ≥ x + 4
17.
Match the system to the graph (solution set is the purple area)
a)
y > -4/5x - 1 and y ≤ 2/3x + 3
b)
y ≥ -4/5x - 1 and y ≤ 2/3x + 3
c)
y < -4/5x - 1 and y < 2/3x + 3
d)
y < -4/5x - 1 and y ≥ 2/3x + 3
18.
JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $66 per week? How much does she make?
a)
b + t < 15
3b + 6t > 66
3b + 6t > 66
b)
b + t > 15
3b + 6t < 66
3b + 6t < 66
c)
3b + 6t > 15
b + t < 66
b + t < 66
d)
3b + 6t < 15
b + t < 66
b + t < 66
19.
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
20.
Solve the following system using the method of your choice.
a)
(1, -5)
b)
(-5, 1)
c)
(-4, 1)
d)
No solution
21.
If I have 18 dimes and quarters that are worth $2.25, which system would represent this?
a)
d + q = 2.25
.10d + .25q = 18
.10d + .25q = 18
b)
d + q = 18
.10d + .25q = 2.25
.10d + .25q = 2.25
c)
18 d = q
.10d + .25q = 2.25
.10d + .25q = 2.25
d)
d+ q = 18
.25d + .10q = 2.25
.25d + .10q = 2.25
22.
What is the system for the two rental cars? Car A cost $28 per day plus insurance of $15 and Car B cost $23 per day plus insurance of $18.
a)
y = 28x + 15
y = 23x + 18
y = 23x + 18
b)
y = 28x + 18
y = 23x +15
y = 23x +15
c)
y= 15x + 28
y = 18x + 23
y = 18x + 23
d)
28x + 23 y = 15
28x + 23y = 18
28x + 23y = 18
23.
Which system of inequalities matches the graph?
a)
y > 2x - 4
y < 2
y < 2
b)
y < 2x - 4
y < 2
y < 2
c)
y > 2x - 4
y < 2
y < 2
d)
y < 2x - 4
y < -2
y < -2
24.
How can I tell if an inequality will have a solid line?
a)
It has an equal sign.
b)
The symbol is greater than.
c)
The symbol has "or equal to."
d)
You just guess.
25.
At Least
a)
<
b)
>
c)
≤
d)
≥
26.
Fewer Than
a)
<
b)
>
c)
≤
d)
≥
27.
Above
a)
<
b)
>
c)
≤
d)
≥
28.
is no less than
a)
<
b)
>
c)
≤
d)
≥
100 %
