Download Unit 8 Review – Systems of Linear Equations

Name: ________________________ Class: ___________________ Date: __________
ID: A
Math 10 - Unit 8 Final Review - Systems of Linear Equations
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which linear system has the solution x = 9 and y = –1?
a. x + 3y = 6
c. x + 2y = 9
2x + 2y = 16
2x + 4y = 18
b. x + 3y = 7
d. 2x + y = 9
2x + y = 15
x+y=6
____
2. Which linear system has the solution x = 2 and y = –4?
a. x + 5y = 7
c. 5x + y = 6
–4x + 2y = –16
2x −4y = –17
b. 2x + 5y = 2
d. x + 5y = 2
–4x + y = 6
2x + 4y = 4
____
3. Which linear system has the solution x = 8 and y = 2.5?
a. 2x + 3y = 23.5
c. 3x + 2y = 8
2x – 2y = 11
x – y = 23.5
b. x + 2y = 8
d. x + 3y = 24.5
2x – 4y = 16
2x – y = 10
____
4. Create a linear system to model this situation:
The perimeter of an isosceles triangle is 42 cm. The base of the triangle is 6 cm longer than each equal side.
a. s + b = 42
b. 2s + b = 42
c. 2b + s = 42
d. 2s + b = 42
b–6=s
b+6=s
s+6=b
s+6=b
____
5. 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 65 points scored.
a. j = 5 + 2a
b. j – 5 = 2a
c. j + 5 = 2a
d. a = 5 + 2j
j + a = 65
j + 2a = 65
j + a = 65
j + a = 65
____
6. 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
c. w = 3s
w + 13 = 2s
w = 2s
b. w = 3s
d. w = 3s
w + 13 = 2(s + 13)
s + 13 = 2(w + 13)
____
7. 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 278 m.
a. l + 35 = w
b. l = w + 35
c. l = w + 35
d. l = w + 35
2l + 2w = 278
2l + 2w = 278
l + w = 278
lw = 278
1
Name: ________________________
____
ID: A
8. Which graph represents the solution of the linear system:
y = –2x + 2
y + 6 = 2x
a.
b.
Graph B
Graph A
c.
d.
2
Graph C
Graph D
Name: ________________________
____
ID: A
9. Which graph represents the solution of the linear system:
–3x – y = –4
3x – y = 2
a.
b.
Graph A
Graph B
c.
d.
3
Graph C
Graph D
Name: ________________________
ID: A
____ 10. Use the graph to solve the linear system:
y = –4x − 2
y + 2 = 2x
a.
b.
(2, 0)
(2, –2)
c.
d.
(0, 0)
(0, –2)
____ 11. Which linear system is represented by this graph?
a) x – y = 2
5x + 7y = 17
b) x – y = 4
5x + 7y = 17
c) x – y = 6
6x + 7y = 17
d) x – y = 8
7x + 5y = 17
a.
System d
b.
System b
c.
4
System a
d.
System c
Name: ________________________
ID: A
____ 12. Express each equation in slope-intercept form.
6
x + y = –121
12
13x + 6y = –2886
a.
b.
y = 222x −242
13
6
y=− x+
13
6
y = −2x −242
y = −2x – 222
c.
d.
y = −2x −242
13
y=− x
6
y = −2x −242
13
y = − x −481
6
____ 13. Use the table of values to determine the solution of this linear system:
6x + y = 3
2x + y = −5
a.
b.
(–9, –9)
(2, –9)
c.
d.
(–9, 2)
(2, 2)
c.
(–8, –30)
d.
(–8, 30)
c.
(8, 10)
d.
(–8, –10)
c.
(–10, –12)
d.
(–12, –10)
____ 14. Use substitution to solve this linear system.
166 2
– x
y=
5
5
14x + 7y = 322
a.
(8, –30)
b.
(8, 30)
____ 15. Use substitution to solve this linear system.
x = 4y – 32
5x + 12y = 160
a.
(8, –10)
b.
(–8, 10)
____ 16. Use substitution to solve this linear system.
x=2+y
9
x + 8y = –141
2
a.
(–12, –12)
b.
(–10, –10)
5
Name: ________________________
ID: A
____ 17. Use substitution to solve this problem:
Tanukah invested a total of $5600 in two bonds. He invested in one bond at an annual interest rate of 6% and
in another bond at an annual interest rate of 8%. After one year, the total interest earned was $410.50. How
much money did Tanukah invest in each bond?
a.
$3725 at 6%,
$1875 at 8%
b.
$1875 at 6%,
$3725 at 8%
c.
$4225 at 6%,
$1375 at 8%
d.
$1375 at 6%,
$4225 at 8%
____ 18. Use substitution to solve this problem:
The perimeter of a rectangular field is 296 m. The length is 52 m longer than the width.
What are the dimensions of the field?
a.
80 m by 68 m
b.
90 m by 58 m
c.
100 m by 48 m
d.
70 m by 78 m
____ 19. Use substitution to solve this problem:
Wai Sen scored 85% on part A of a math test and 95% on part B of the math test. Her total mark for the test
was 94. The total mark possible for the test was 104.
How many marks is each part worth?
a.
b.
Part A: 56 marks; part B: 56 marks
Part A: 48 marks; part B: 48 marks
____ 20. Use substitution to solve this linear system:
x – y = 17
1
4
97
x+ y=−
2
5
10
a. x = 3; y = 17
b. x = –14; y = –14
c.
d.
Part A: 56 marks; part B: 48 marks
Part A: 48 marks; part B: 56 marks
c.
x = 3; y = –14
d.
x = 3; y = 3
d.
35
d.
21
____ 21. The solution of this linear system is (–6, y). Determine the value of y.
3
39
x– y=−
4
4
8
31
x–y=−
9
3
a.
15
b.
25
c.
5
____ 22. The solution of this linear system is (–31, y). Determine the value of y.
1
1
83
x– y=−
2
4
4
6
480
x – 2y = −
7
7
a.
26
b.
31
c.
6
41
Name: ________________________
ID: A
____ 23. Use an elimination strategy to solve this linear system.
20x − 15y = 50
10x + 25y = 90
a. x = 14 and y = 2
c. x = 4 and y = 2
37
26
b. x =
and y =
d. x = 2 and y = 4
7
7
____ 24. Use an elimination strategy to solve this linear system.
9x − 6y = 15
6x + 21y = 60
a. x = 3 and y = −2
c. x = 3 and y = 2
1
14
b. x = and y =
d. x = −3 and y = −2
5
5
____ 25. Use an elimination strategy to solve this linear system.
2
3
m + n = 16
3
4
1
3
− m + n = 18
2
8
a. m = −12 and n = 32
c. m = 12 and n = −32
201
52
32
b. m =
and n =
d. m = −12 and n =
10
15
3
____ 26. Model this situation with a linear system:
Frieda has an 11% silver alloy and a 25% silver alloy. Frieda wants to make 23 kg of an alloy that is 43%
silver.
c. s + t = 23 and 0.11s + 0.25t = 0.43
a. s + t = 0.43 and 0.11s + 0.25t = 23
b. s + t = 43 and 0.11s + 0.25t = 23
d. s + t = 23 and 0.11s + 0.25t = 9.89
____ 27. Use an elimination strategy to solve this linear system.
20x − 24y = −52
8x + 32y = 104
a. x = −1 and y = −3
c. x = 1 and y = −3
b. x = 3 and y = 1
d. x = 1 and y = 3
____ 28. Use an elimination strategy to solve this linear system.
2
1
x + y = −11
3
7
1
1
x − y = −10
7
3
a. x = −21 and y = 21
c. x = 21 and y = −21
b. x = 21 and y = 21
d. x = −21 and y = −21
____ 29. Without graphing, determine the slope of the graph of the equation:
7x + 4y = 12
7
7
a.
b. –
c. 4
4
4
7
d.
7
Name: ________________________
ID: A
____ 30. Without graphing, determine which of these equations represent parallel lines.
i) –7x + 7y = 10
ii) –5x + 7y = 10
iii) –3x + 7y = 10
iv) –7x + 7y = 12
a. ii and iii
b. i and ii
c. i and iv
d. i and iii
____ 31. Without graphing, determine the equation whose graph intersects the graph of –4x + 3y = 10
exactly once.
i) –4x + 3y = 12
ii) –16x + 12y = 40
iii) –2x + 3y = 10
a.
iii
b.
none
c.
ii
d.
i
____ 32. Determine the number of solutions of the linear system:
3x – 7y = 43
–9x + 21y = 39
a.
b.
one solution
no solution
c.
d.
two solutions
infinite solutions
____ 33. Determine the number of solutions of the linear system:
2x – 3y = 23
2x – 3y = 5
a.
b.
no solution
infinite solutions
c.
d.
two solutions
one solution
____ 34. Determine the number of solutions of the linear system:
15x + 5y = 310
17x – 4y = 593
a.
b.
no solution
one solution
c.
d.
two solutions
infinite solutions
____ 35. The first equation of a linear system is 9x + 6y = 159. Choose a second equation to form a linear system with
infinite solutions.
i) 9x + 6y = –318
ii) –18x – 12y = –318 iii) –18x + 6y = –318 iv) –18x + 6y = 255
a.
Equation iii
b.
Equation iv
c.
Equation i
d.
Equation ii
____ 36. The first equation of a linear system is 7x + 12y = 158. Choose a second equation to form a linear system
with exactly one solution.
i) 7x + 12y = –316
ii) –14x – 24y = –316 iii) –14x + 12y = –316 iv) –14x – 24y = 0
a.
Equation iii
b.
Equation i
c.
8
Equation ii
d.
Equation iv
Name: ________________________
ID: A
____ 37. The first equation of a linear system is –8x + 12y = –48. Choose a second equation to form a linear system
with no solution.
i) –8x + 12y = 240
ii) 40x – 60y = 240
iii) 40x + 12y = 240
iv) 40x + 60y = 0
a.
Equation iv
b.
Equation ii
c.
Equation iii
d.
____ 38. For what value of k does the linear system below have infinite solutions?
4
x + y = 11
5
kx + 2y = 22
4
8
a. 22
b.
c.
d.
5
5
Short Answer
39. Solve this linear system by graphing.
–3x – 2y = 12
–x + y = –6
9
Equation i
0
Name: ________________________
ID: A
40. Solve this linear system by graphing.
y = –2
–3x + y = 7
41. a)
Write a linear system to model this situation:
A hockey coach bought 20 pucks for a total cost of $47.5. The pucks used for practice cost
$2.00 each, and the pucks used for games cost $2.75 each.
b) Use a graph to solve this problem:
How many of each type of puck did the coach purchase?
10
Name: ________________________
ID: A
42. Use substitution to solve this linear system:
5x + y = −192
−5x + 4y = 107
43. Use substitution to solve this linear system:
3
x + y = –49
4
–4x + 2y = 136
44. Create a linear system to model this situation. Then use substitution to solve the linear system to solve the
problem.
At the local fair, the admission fee is $6.00 for an adult and $3.50 for a youth. One Saturday, 187 admissions
were purchased, with total receipts of $834.50. How many adult admissions and how many youth admissions
were purchased?
45. Use an elimination strategy to solve this linear system.
6x + 6y = 618
3x − 3y = 81
46. Determine the number of solutions of this linear system.
15x + 20y = –5
17x + 11y = 286
47. For what values of k does the linear system below have:
a) infinite solutions?
b) one solution?
c) no solution?
4
x + y = 15
5
kx + 3y = 45
Problem
48. a) Write a linear system to model this situation.
Mrs. Cheechoo paid $150 for one-day tickets to Silverwood Theme Park for herself, her husband, and 2
children. Next month, she paid $405 for herself, 4 adults, and 6 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?
11
ID: A
Math 10 - Unit 8 Final Review - 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.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
A
C
A
D
A
B
B
B
A
D
C
D
B
B
C
C
B
C
D
C
C
D
C
C
A
D
D
A
B
C
A
B
A
B
D
A
D
C
1
ID: A
SHORT ANSWER
39. (0, –6)
40. (–3, –2)
2
ID: A
41. a)
b)
p + g = 20
2p + 2.75g = 47.5
The team purchased 10 pucks for practice and
10 pucks for games.
42. x = –35; y = –17
43. x = –40; y = –12
44. Let a represent the number of adult admissions, and y represent the number of youth admissions purchased.
a + y = 187
6a + 3.5y = 834.5
72 adult admissions and 115 youth admissions were purchased.
45. x = 65
y = 38
46. One solution
12
47. a) k =
5
12
b) k ≠
5
c) For the system to have no solution, the lines must be parallel; that is, their slopes are equal and their
y-intercepts are different. But the lines have the same y-intercept, so they cannot be parallel.
3
ID: A
PROBLEM
48. a) Let a represent the cost in dollars for a one-day adult ticket, and c represent the cost in dollars for a
one-day child ticket.
Then, a system of equations is:
2a + 2c = 150
5a + 6c = 405
b)
Since the intersection point is at (45, 30), the cost of a one-day adult ticket is $45, and the cost of a
one-day child ticket is $30.
4