Name: 
 

Math 10 Foundations LG 12 Practice Quiz 3


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Which linear system has the solution x = 8 and y = 2.5?
a.
2x + 2y = 21
2x – 2y = 11
c.
2x + 2y = 8
x – y = 21
b.
x + 2y = 8
2x – 4y  = 16
d.
x + 3y = 22
2x – y = 10
 

 2. 
Which graph represents the solution of the linear system:
–3x – y = –5
4x – y = mc002-1.jpg 
mc002-2.jpgmc002-3.jpg
mc002-4.jpgmc002-5.jpg
a.
Graph A
c.
Graph C
b.
Graph B
d.
Graph D
 

 3. 
Two life insurance companies determine their premiums using different formulas:
Company A: p = 2a + 24
Company B: p = 2.25a + 13, where p represents the annual premium, and a represents the client’s age.
Use the graph to determine the age at which both companies charge the same premium.
mc003-1.jpg


     
a.
62 years
b.
 24 years
c.
59 years
d.
44 years
 

 4. 
Express each equation in slope-intercept form.
–2x + 4y = 68
13x + 4y = 284
a.
y = mc004-1.jpgx – mc004-2.jpg
y = mc004-3.jpgx – mc004-4.jpg
c.
y = mc004-9.jpgx + mc004-10.jpg
y = mc004-11.jpgx + mc004-12.jpg
b.
y = mc004-5.jpgx + mc004-6.jpg
y = mc004-7.jpgx + mc004-8.jpg
d.
y = mc004-13.jpgx mc004-14.jpg
y = mc004-15.jpgx mc004-16.jpg
 

 5. 
Express each equation in slope-intercept form.
x + mc005-1.jpgy = –83
12x + 4y = –1772
a.
y = mc005-2.jpgx mc005-3.jpg
y = mc005-4.jpgx + mc005-5.jpg
c.
y = mc005-10.jpgx mc005-11.jpg
y = mc005-12.jpgx
b.
y = mc005-6.jpgx mc005-7.jpg
y = mc005-8.jpgx – mc005-9.jpg
d.
y = mc005-13.jpgx mc005-14.jpg
y = mc005-15.jpgx mc005-16.jpg
 

 6. 
Create a linear system to model this situation:
A rectangular field is 35 m longer than it is wide. The length of the fence around
the perimeter of the field is 290 m.
a.
l + 35 = w
2l + 2w = 290
b.
l = w + 35
2l + 2w = 290
c.
l = w + 35
l + w = 290
d.
l = w + 35
lw = 290
 

 7. 
Write a linear system to model this situation. Then verify which of the given solutions is correct.
A crate of 32 grapefruit has a total mass of 4.648 kg.
When 9 grapefruit are removed, the total mass is 3.622 kg.
Verify the mass of the crate and the average mass of one grapefruit.
A. mc007-1.jpg       B. mc007-2.jpg            C. mc007-3.jpg      D. mc007-4.jpg
i)       The crate has a mass of 1 kg, and the mass of one grapefruit is 114 g.
ii)       The crate has a mass of  1.2 kg, and the mass of one grapefruit is 114.2 g.
iii)       The crate has a mass of  1 kg, and the mass of one grapefruit is 114.2 g.
iv)       The crate has a mass of  1.2 kg, and the mass of one grapefruit is 57 g.
a.
Part A-i
c.
Part B-iii
b.
Part C-ii
d.
Part D-iv
 

 8. 
Which linear system is represented by this graph?
a)       x – y = 5
5x + 6y = 18

b)      x – y = 7
5x + 6y = 18

c)       x – y = 9
6x + 6y = 18

d)      x – y = 11
6x + 5y = 18
mc008-1.jpg




     
a.
System d
b.
System b
c.
System a
d.
System c
 

 9. 
Which linear system is represented by this graph?
a)       2x – 5y = –16
x = 1

b)      2x + 5y = 16
2x – 5y = 16

c)      2x – 5y = 16
x – mc009-1.jpgy = –1

d)      2x + 5y = 16
x = –1
mc009-2.jpg




     
a.
System a
b.
System d
c.
System b
d.
System c
 

 10. 
Determine the solution of the linear system represented by this graph.
a) (3, 5.3)

b) (5.3, 3)

c) ( 5.3, –3)

d) (–4, 5.3)

mc010-1.jpg





     
a.
d
b.
a
c.
c
d.
b
 

Short Answer
 

 11. 
Quincy used this linear system to represent a situation involving a collection of $5 bills and $10 bills:
f + t = 70
5f + 10t = 575
a)       What problem might Quincy have written?
b)       What does each variable represent?
 

 12. 
Create a linear system to model this situation:
The cost of admission to the museum is $5.50 for adults and $3.50 for students.
Yesterday, 100 admissions were sold, and the receipts were $424.00.
 

 13. 
Solve this linear system by graphing.
–3x – 2y = 16
–x + y = –8
sa013-1.jpg
 

 14. 
Use graphing technology to solve this linear system.
Where necessary, write the coordinates to the nearest tenth.
–3x – 5y = 12
–x + y = –10
 

Problem
 

 15. 
a)       Write a linear system whose solution is: x = 5, y = –5.
b)       Is there more than one linear system with this solution? Explain.
 

 16. 
a)       Write a linear system to model this situation.
Mrs. Cheechoo paid $155 for one-day tickets to Silverwood Theme Park for herself, her husband, and 3 children. Next month, she paid $285 for herself, 3 adults, and 5 children.
b)      Use a graph to solve this problem:
What are the prices of a one-day ticket for an adult and for a child?
 

 17. 
a)       Write a linear system to model this situation:
A large tree removes 1.5 kg of pollution from the air each year. A small tree removes 0.04 kg each year. An urban forest has 1650 large and small trees. Together, these trees remove 1818 kg of pollution each year.
b)       Use graphing technology to solve this problem:
How many of each size of tree are in the forest?
c)      Verify the solution.
 



 
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