Download ExamView - Unit8REVIEW_Systems.tst

Name: ________________________ Class: ___________________ Date: __________
Math 10 - Unit 8 REVIEW WORKSHEET - Systems of Linear Equations
Multiple Choice
Identify the choice that best answers the question.
____
1. Without graphing, determine the equation whose graph intersects the graph of –7x + 7y = 10
exactly once.
i) –7x + 7y = 12
ii) –28x + 28y = 40
iii) –5x + 7y = 10
a.
ii
b.
i
c.
iii
d.
____
2. Which linear system has the solution x = 2 and y = –2?
a. x + 2y = 2
c. x + 4y = –6
2x + 4y = 4
2x + 2y = 0
b. x + 3y = –5
d. 2x + y = 2
2x + y = –1
x + y = –6
____
3. For what value of k does the linear system below have infinite solutions?
5
x + y = 12
6
kx + 2y = 24
5
a. 24
b. 0
c.
d.
6
____
no solution
infinite solutions
c.
d.
one solution
2 solutions
5. Two lines in a linear system have a different slope, but the same y-intercepts.
How many solutions does the linear system have?
a.
b.
____
5
3
4. Determine the number of solutions of the linear system:
4x + 5y = 102
–24x – 30y = –612
a.
b.
____
none
two solutions
no solution
c.
d.
infinite solutions
one solution
6. Without graphing, determine the slope of the graph of the equation:
7x + 4y = 11
7
7
a.
b. –
c. 7
4
4
1
d.
4
ID: A
Name: ________________________
____
7. Use the table of values to determine the solution of this linear system:
x = y+2
4x + 5y = −10
a.
b.
____
(0,–2)
(–2, –2)
c.
d.
(0, 0)
(–2, 0)
c.
d.
(0, –4)
(2, –2)
8. Use the graph to solve the linear system:
y = –5x − 4
y + 4 = 3x
a.
b.
____
ID: A
(2, –4)
(0, –2)
9. Create a linear system to model this situation:
In a board game, Judy scored 5 points more than twice the number of points Ann scored.
There was a total of 35 points scored.
a. j – 5 = 2a
b. j = 5 + 2a
c. j + 5 = 2a
d. a = 5 + 2j
j + 2a = 35
j + a = 35
j + a = 35
j + a = 35
2
Name: ________________________
ID: A
____ 10. The solution of this linear system is (–5, y). Determine the value of y.
81
4
x– y=−
5
5
5
109
x–y=−
6
6
a.
34
b.
24
c.
14
____ 11. Which graph represents the solution of the linear system:
y = –2x
y + 5 = 3x
a.
b.
Graph A
Graph D
c.
d.
3
Graph C
Graph B
d.
44
Name: ________________________
ID: A
____ 12. Determine the number of solutions of the linear system:
3x – 5y = 43
–9x + 15y = 21
a.
b.
two solutions
infinite solutions
c.
d.
no solution
one solution
____ 13. Without graphing, determine the equation whose graph intersects the graph of –6x + 6y = 11
exactly once.
i) –6x + 6y = 13
ii) –24x + 24y = 44
iii) –4x + 6y = 11
a.
ii
b.
i
c.
iii
d.
none
____ 14. Which linear system has the solution x = 0 and y = 7?
a. x + 2y = 0
c. x + 2y = 14
2x + 4y = 0
3x + 3y = 21
b. x + 3y = 15
d. 2x + y = 0
2x + y = 20
x + y = 14
____ 15. For what value of k does the linear system below have infinite solutions?
6
x + y = 13
7
kx + 2y = 26
6
a. 26
b. 0
c.
d.
7
12
7
____ 16. For what value of k does the linear system below have infinite solutions?
2
x + y = 10
3
kx + 2y = 20
2
a. 20
b. 0
c.
d.
3
4
3
____ 17. Determine the number of solutions of the linear system:
14x + 7y = 315
16x – 2y = 610
a.
b.
no solution
one solution
c.
d.
4
two solutions
infinite solutions
Name: ________________________
ID: A
Short Answer Please clearly show your process and box your final answer for full marks.
18. Determine the number of solutions of this linear system.
2x – 3y = 5
-6x +9y = -15
19. Determine the number of solutions of this linear system.
2x – 3y = 5
10x - 15y = 20
20. Determine the number of solutions of this linear system.
2x – 3y = 5
10x - 20y = 7
21. Create a linear system to model this situation. Then use substitution to solve the linear system to solve the
problem.
Kim has been saving dimes and nickels to buy a new toy. She has a total of 32 dimes and nickels, with a
value of $2.50. How many of each type of coin does Kim have?
5
Name: ________________________
ID: A
22. A submarine cruises underwater at 10 km/h and on the surface at 20 km/h. The submarine travels a distance
of 400 km in 25 h. A linear system that models this situation is:
u + s = 25
10u + 20s = 400
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:
i) How long did the submarine travel underwater?
ii) How long did it travel on the surface?
6
Name: ________________________
ID: A
23. Use an elimination strategy to solve this linear system.
8x + 12y = 0
4x + 20y = 28
24. Use an elimination strategy to solve this linear system.
2x + 2y = 206
x − y = 27
25. Create a linear system to model this situation:
The perimeter of a rectangle is 237 ft. When its width is tripled, the perimeter increases by 66 ft.
7
Name: ________________________
ID: A
26. Solve this linear system by graphing.
–3x – 3y = 15
–x + y = –5
8
Name: ________________________
ID: A
27. Create a linear system to model this situation:
The cost of admission to the museum is $7.25 for adults and $5.25 for students.
Yesterday, 139 admissions were sold, and the receipts were $815.75.
28. Use substitution to solve this linear system:
6
x + y = –67
7
–3x + 6y = 81
29. Use substitution to solve this linear system:
2x + y = −103
−4x + 3y = 141
9
Name: ________________________
ID: A
30. Solve this linear system by graphing.
y = –4
–3x + y = 5
10
ID: A
Math 10 - Unit 8 REVIEW WORKSHEET - Systems of Linear Equations
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
C
C
D
B
D
B
A
C
B
C
A
C
C
C
D
D
B
SHORT ANSWER
18.
19.
20.
21.
Infinite number of solutions
No solutions
One solution
Let d represent the number of dimes and n represent the number of quarters.
d + n = 32
10d + 5n = 250
Kim has 18 dimes and 14 nickels.
22. a)
b)
(10, 15)
23.
x = −3 and y = 2
1
ID: A
24. x = 65
y = 38
25. 2l + 2w = 237
2l + 6w = 303
26. (0, –5)
27. Let a represent the number of adult admissions
Let s represent the number of student admissions.
a + s = 139
7.25a + 5.25s = 815.75
28. x = –55; y = –14
29. x = –45; y = –13
30. (–3, –4)
2