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Systems of linear equations - word problems

Total questions: 11

Worksheet time: 53mins

Name
Class
Date
1.
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
b)
3x + 2y = 450
2x + 4y = 315
c)
2x + 2y = 315
3x + 4y = 450
2.
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
3.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
4.
What kind of lines have no solution to a system of equations
a)
Parallell Lines
b)
Overlapping lines
c)
Intersecting Lines
d)
Skew Lines
5.

Which system of equations represent the following problem? Paloma, Devon, and Anthony went shopping for Halloween treats. Paloma bought 3 chocolate pumpkins, 4 masks and 8 candy witches. She spent $36.65. Anthony bought 5 chocolate pumpkins, 3 masks and 10 candy witches. He spent $37.50. Devon bought 4 chocolate pumpkins, 5 masks, and 6 candy witches. He spent $43.45.

a)
b)
c)
d)
6.
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
b)
1.5x+0.5y=78.5
1.5x+0.5y=87
c)
x+y=78.5
1.5x+0.5y=87
d)
x+y=78.5
x+y=87
7.
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
b)
3s + 1c = 38
3s + 2c = 52
c)
s + c = 38
s + c = 52
d)
3s + 3c = 38
1s + 2c = 52
8.
Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins and it came to $6.60.  Which system of equations could be used to find the exact number of dimes and nickels? 
a)
d + n = 6.60
.10d + .05n = 80
b)
d + n = 80
d + n = 6.60
c)
d + n = 80
.10d + .05n = 6.60
d)
d + n = 80
.05d + .10n = 6.60
9.

The difference between Alex's age and Erin's age is 7. The sum of their ages is 27 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

a)

x - y = 27

x + y = 7

b)

x - y = 7

x + y = 27

c)

x + y = 7

x + y = 27

d)

x + y = 34

x - y = 20

10.

Christian originally ordered 4 boxes of blue T-shirts and 3 boxes of red T-shirts, which cost a total of $134. After he ran out, Christian spent $120 on 3 boxes of blue T-shirts and 3 boxes of red T-shirts.


Let x = the price of a box of blue T-shirts

Let y = the price of a box of red T-shirts


Which system represents this situation?

a)

x+y=134

x+y=120

b)

3x+3y=134

4x+3y=120

c)

4x+3y=134

3x+3y=120

d)

7xy=134

6xy=120

11.

Josh is thinking of two numbers. Their sum is -10 and their difference is -2.


Let x = a number

Let y = another number.


Which system of equations represents the situation?

a)

x - y = -10

x + y = -2

b)

x = -2

y = 5

c)

x + y = -2

x - y = -10

d)

x + y = -10

x - y = -2