Math 10 Foundations LG 14 Unit 4 Practice Test 4

Name:

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

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

Which graph represents the solution of the linear system:
y = –2x

y + 6 = 2x

a.	Graph B	c.	Graph C
b.	Graph A	d.	Graph D

Use the graph to approximate the solution of the linear system:

a.	(–3, 0.2)	c.	(0.2, –3)
b.	(0, –2.8)	d.	(–2.8, 0)

Car A left Calgary at 8 A.M. to travel 500 mi. to Regina, at an average speed of 63 mph.
Car B left Regina at the same time to travel to Calgary at an average speed of
37 mph. A linear system that models this situation is:
d = 500 – 63t
d = 37t,
where d is the distance in miles from Regina, and t is the time in hours since 8 A.M. Which graph would you use to determine how far the cars are from Regina when they meet? What is this distance?

Graph C:
195.8 mi.

Graph D:
200 mi.

Graph A:
185 mi.

Graph B:
92.5 mi.

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.

62 years

24 years

59 years

44 years

Create a linear system to model this situation:
A woman is 3 times as old as her son. In thirteen years, she will be 2 times as old as her son will be.

a.	w = s + 3 w + 13 = 2s	c.	w = 3s w = 2s
b.	w = 3s w + 13 = 2(s + 13)	d.	w = 3s s + 13 = 2(w + 13)

Create a linear system to model this situation:
Tickets for a school play cost $8 for adults and $4.75 for students.
There were ten more student tickets sold than adult tickets, and a total of $1399 in ticket sales was collected.

a.	8a + 4.75s = 1399 s = a + 10	c.	8a + 4.75s = 1399 a = s + 10
b.	8a + 4.75s = 1399 a + s = 10	d.	4.75a + 8s = 1399 s = a + 10

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.

      B.             C.       D.
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

Use the graph to solve the linear system:
y = –3x – 5
y = 3x

a.	(1, –2)	c.	(1, 0)
b.	(–1, 0)	d.	(–1, –2)

10.

Which linear system is represented by this graph?

a) x – y = 3 6x + 5y = 14 b) x + y = 5 6x + 5y = 14 c) x + y = 7 7x + 5y = 14 d) x + y = 9 5x + 6y = 14

System a

System b

System c

System d

11.

Determine the solution of the linear system represented by this graph.

a) (2, 3.8) b) (3.8, 2) c) (–3, 3.8) d) (–2, 3.8)

12.

Use substitution to solve this linear system.
y =

– x
13x + 5y = 178

(6, –20)

(6, 20)

(–6, –20)

(–6, 20)

13.

Use substitution to solve this linear system:
x – y = 18

x +

y =

x = 4; y = 18

x = –14; y = –14

x = 4; y = –14

x = 4; y = 4

14.

The solution of this linear system is (–3, y). Determine the value of y.
x –

y =

x – y =

15.

The solution of this linear system is (–28, y). Determine the value of y.

x –

y =

x – 4y =

16.

Use an elimination strategy to solve this linear system.

a.	and	c.	and
b.	and	d.	and

17.

Use an elimination strategy to solve this linear system.

a.	and	c.	and
b.	and	d.	and

18.

Which linear system is modelled by these balance scales? (Each small square on the right side of the balance scales represents 2 kg.)

a.	and	c.	and
b.	and	d.	and

19.

Without graphing, determine which of these equations represent parallel lines.
i) –6x + 6y = 12
ii) –4x + 6y = 12
iii) –2x + 6y = 12
iv) –6x + 6y = 14

ii and iii

i and ii

i and iv

i and iii

20.

Determine the number of solutions of the linear system:
14x – 5y = 123
14x – 5y = 73

a.	no solution	c.	two solutions
b.	infinite solutions	d.	one solution

Short Answer

21.

A submarine cruises underwater at 20 km/h and on the surface at 30 km/h. The submarine travels a distance of 650 km in 25 h. A linear system that models this situation is:
u + s = 25
20u + 30s = 650
where u represents the time in hours cruising underwater, and s represents the time in hours cruising on the surface.
a) Graph the linear system above.
b) Use the graph to solve the problem:

How long did the submarine travel underwater, and how long did it travel on the surface?

22.

a) Write a linear system to model this situation:

A hockey coach bought 25 pucks for a total cost of $70. The pucks used for practice cost

$2.50 each, and the pucks used for games cost $3.25 each.

b) Use a graph to solve this problem:

How many of each type of puck did the coach purchase?

23.

Fill in the each blank below with the correct integer.

System A -____: -____:	System B 7x + 6y = –376 –4x – 6y = 256

24.

Use an elimination strategy to solve this linear system.

25.

The first equation of a linear system is

. Write a second equation to form a linear system with infinite solutions.

Problem

26.

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.

27.

a) Write a linear system to model the situation:

A sports club charges an initiation fee and a monthly fee. At the end of 5 months, a member had paid a total of $450. At the end of 10 months, she had paid a total of $500.

b) Solve the linear system by substitution to solve the related problem:

What are the initiation fee and the monthly fee?

28.

a) Model this situation with a linear system:

To rent a car, a person is charged a daily rate and a fee for each kilometre driven. When Chena rented a car for 15 days and drove 800 km, the charge was $715.00. When she rented the same car for 25 days and drove 2250 km, the charge was $1512.50.

b) Determine the daily rate and the fee for each kilometre driven. Verify the solution.

29.

Use the equation

as an equation in three different linear systems. Write a second equation so that each system has a different number of solutions. Explain what you did for each system.

30.

Determine the number of solutions of this linear system.